Need help in my STAT Class. Please see attachments for questions, less than 35 questions. Example of one question: Police response time to an emergency call is the difference between the time the ca

1. Consider a binomial experiment with n = 4 trials where the probability of success on a single trial is p = 0.15.

 (Round your answers to three decimal places.)

(a) Find 

P(r = 0).

(b) Find 

P(r ≥ 1) by using the complement rule.

2. Richard has just been given a 4-question multiple-choice quiz in his history class. Each question has five answers, of which only one is correct. Since Richard has not attended class recently, he doesn't know any of the answers. Assuming that Richard guesses on all four questions, find the indicated probabilities. (Round your answers to three decimal places.)

(a) What is the probability that he will answer all questions correctly?

(b) What is the probability that he will answer all questions incorrectly?

(c) What is the probability that he will answer at least one of the questions correctly? Compute this probability two ways. First, use the rule for mutually exclusive events and the probabilities shown in the binomial probability distribution table.

Then use the fact that P(r ≥ 1) = 1 − P(r = 0).

Compare the two results. Should they be equal? Are they equal? If not, how do you account for the difference?

They should be equal, but differ substantially.

They should be equal, but may not be due to table error.  

  They should not be equal, but are equal.

They should be equal, but may differ slightly due to rounding error.

(d) What is the probability that Richard will answer at least half the questions correctly?

3. The one-time fling! Have you ever purchased an article of clothing (dress, sports jacket, etc.), worn the item once to a party, and then returned the purchase? This is called a one-time fling. About 15% of all adults deliberately do a one-time fling and feel no guilt about it! In a group of ten adult friends, what is the probability of the following? (Round your answers to three decimal places.)

(a) no one has done a one-time fling

(b) at least one person has done a one-time fling

(c) no more than two people have done a one-time fling

4. Trevor is interested in purchasing the local hardware/sporting goods store in the small town of Dove Creek, Montana. After examining accounting records for the past several years, he found that the store has been grossing over $850 per day about 70% of the business days it is open. Estimate the probability that the store will gross over $850 for the following. (Round your answers to three decimal places.)

(a) at least 3 out of 5 business days

(b) at least 6 out of 10 business days

(c) fewer than 5 out of 10 business days

(d) fewer than 6 out of the next 20 business days

If the outcome described in part (d) actually occurred, might it shake your confidence in the statement p = 0.70? Might it make you suspect that p is less than 0.70? Explain.

Yes. This is unlikely to happen if the true value of p is 0.70.Yes. This is likely to happen if the true value of p is 0.70.    No. This is unlikely to happen if the true value of p is 0.70.No. This is likely to happen if the true value of p is 0.70.

(e) more than 17 out of the next 20 business days

If the outcome described in part (e) actually occurred, might you suspect that p is greater than 0.70? Explain.

Yes. This is unlikely to happen if the true value of p is 0.70.Yes. This is likely to happen if the true value of p is 0.70.    No. This is unlikely to happen if the true value of p is 0.70.No. This is likely to happen if the true value of p is 0.70.

5. Are your finances, buying habits, medical records, and phone calls really private? A real concern for many adults is that computers and the Internet are reducing privacy. A survey conducted by Peter D. Hart Research Associates for the Shell Poll was reported in USA Today. According to the survey, 52% of adults are concerned that employers are monitoring phone calls. Use the binomial distribution formula to calculate the probability of the following.

(a) Out of six adults, none is concerned that employers are monitoring phone calls. (Round your answer to three decimal places.)

(b) Out of six adults, all are concerned that employers are monitoring phone calls. (Round your answer to three decimal places.)

(c) Out of six adults, exactly four are concerned that employers are monitoring phone calls. (Round your answer to three decimal places.)

6. Look at the two normal curves in the figures below.

Which has the larger standard deviation?

Figure (a)Figure (b)    

What is the mean of the curve in Figure (a)?

What is the mean of the curve in Figure (b)?

7. (a) What percentage of the area under the normal curve lies to the left of μ?
 %
(b) What percentage of the area under the normal curve lies between μ − σ and μ + σ?
 %
(c) What percentage of the area under the normal curve lies between μ − 3σ and μ + 3σ?
 %

8. What percentage of the area under the normal curve lies as given below?

(a) to the right of μ
 %
(b) between μ – 2σ and μ + 2σ
 %
(c) to the right of μ + 3σ (Use 2 decimal places.)
 %

9. Assuming that the heights of college women are normally distributed with mean 63 inches and standard deviation 2.4 inches, answer the following questions. (Hint: Use the figure below with mean μ and standard deviation σ.)

(a) What percentage of women are taller than 63 inches?
 %
(b) What percentage of women are shorter than 63 inches?
 %
(c) What percentage of women are between 60.6 inches and 65.4 inches?
 %
(d) What percentage of women are between 58.2 and 67.8 inches?
 %

10. The incubation time for a breed of chicks is normally distributed with a mean of 21 days and standard deviation of approximately 1 day. Look at the figure below and answer the following questions. If 1000 eggs are being incubated, how many chicks do we expect will hatch in the following time periods? (Note: In this problem, let us agree to think of a single day or a succession of days as a continuous interval of time. Assume all eggs eventually hatch.)

(a) in 19 to 23 days
 chicks
(b) in 20 to 22 days
 chicks
(c) in 21 days or fewer
 chicks
(d) in 18 to 24 days
 chicks

11. A normal distribution has μ = 28 and σ = 5.

(a) Find the z score corresponding to 

x = 23.

(b) Find the z score corresponding to 

x = 42.

(c) Find the raw score corresponding to 

z = −3.

(d) Find the raw score corresponding to 

z = 1.7.

12. Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.)

P(z ≤ −0.24)

 = 
Shade the corresponding area under the standard normal curve.

14. Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.)
P(z ≤ 1.24) = 
Shade the corresponding area under the standard normal curve.

15. Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.)
P(z ≥ 1.31) = 
Shade the corresponding area under the standard normal curve.

16. Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.)

P(−1.20 ≤ z ≤ 2.63)

 = 
Shade the corresponding area under the standard normal curve.

18. Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.)

P(−2.18 ≤ z ≤ −0.44) = 

Shade the corresponding area under the standard normal curve.

19. Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

μ = 15.9; σ = 4.2

P(10 ≤ x ≤ 26) = 

20. Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

μ = 38; σ = 14

P(50 ≤ x ≤ 70) = 

21. Find z such that 5.4% of the standard normal curve lies to the right of z. (Round your answer to two decimal places.)
z = 
Sketch the area described.

22. Find z such that 5% of the standard normal curve lies to the left of z. (Round your answer to three decimal places.)
z = 
Sketch the area described.

23. A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean μ = 89 and standard deviation σ = 22. Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.)

(a) x is more than 60

(b) x is less than 110

(c) x is between 60 and 110

(d) x is greater than 125 (borderline diabetes starts at 125)

24. Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. Let x be a random variable that represents the number of milligrams of porphyrin per deciliter of blood. In healthy circles, x is approximately normally distributed with mean μ = 38 and standard deviation σ = 13. Find the following probabilities. (Round your answers to four decimal places.)

(a) x is less than 60

(b) x is greater than 16

(c) x is between 16 and 60

(d) x is more than 60 (This may indicate an infection, anemia, or another type of illness.)

25. Quick Start Company makes 12-volt car batteries. After many years of product testing, the company knows that the average life of a Quick Start battery is normally distributed, with a mean of 44.6 months and a standard deviation of 7.3 months.

(a) If Quick Start guarantees a full refund on any battery that fails within the 36-month period after purchase, what percentage of its batteries will the company expect to replace? (Round your answer to two decimal places.)
 %
(b) If Quick Start does not want to make refunds for more than 13% of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?
 months

26.

Let's use the following notation for the various events: W = washing oil off within 5 minutes, A = washing oil off after 5 minutes, N = no reaction, M = mild reaction, S = strong reaction. Find the following probabilities for a person selected at random from this sample of 1000 subjects. (Use 3 decimal places.)

26. A stationary store has decided to accept a large shipment of ball-point pens if an inspection of 15 randomly selected pens yields no more than two defective pens.

(a) Find the probability that this shipment is accepted if 5% of the total shipment is defective. (Use 3 decimal places.)

(b) Find the probability that this shipment is not accepted if 20% of the total shipment is defective. (Use 3 decimal places.)

27. According to Harper's Index, 55% of all federal inmates are serving time for drug dealing. A random sample of 16 federal inmates is selected.

(a) What is the probability that 9 or more are serving time for drug dealing? (Round your answer to three decimal places.)

(b) What is the probability that 2 or fewer are serving time for drug dealing? (Round your answer to three decimal places.)

(c) What is the expected number of inmates serving time for drug dealing? (Round your answer to one decimal place.)

28. Given that x is a normal variable with mean μ = 45 and standard deviation σ = 6.9, find the following probabilities. (Round your answers to four decimal places.)

(a)  P(x ≤ 60)

(b)  P(x ≥ 50)

(c)  P(50 ≤ x ≤ 60)

29. Find z such that 23% of the area under the standard normal curve lies to the right of z. (Round your answer to two decimal places.)

30. The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of 9.9 minutes and a standard deviation of 2.0 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows. (Round your answers to four decimal places.)

(a) less than 10 minutes

(b) longer than 5 minutes

(c) between 8 and 15 minutes

31. Many people consider their smart phone to be essential! Communication, news, Internet, entertainment, photos, and just keeping current are all conveniently possible with a smart phone. However, the battery better be charged or the phone is useless. Battery life of course depends on the frequency, duration, and type of use. One study involving heavy use of the phones showed the mean of the battery life to be 9.75 hours with a standard deviation of 3.5 hours. Then the battery needs to be recharged. Assume the battery life between charges is normally distributed.

(a) Find the probability that with heavy use, the battery life exceeds 10 hours. (Round your answer to four decimal places.)

(b) You are planning your recharging schedule so that the probability your phone will die is no more than 5%. After how many hours should you plan to recharge your phone? (Round your answer to the nearest tenth of an hour.)
 hours

32. Sociologists say that 80% of married women claim that their husband's mother is the biggest bone of contention in their marriages (sex and money are lower-rated areas of contention). Suppose that six married women are having coffee together one morning. Find the following probabilities. (Round your answers to three decimal places.)

(a) All of them dislike their mother-in-law.

(b) None of them dislike their mother-in-law.

(c) At least four of them dislike their mother-in-law.

(d) No more than three of them dislike their mother-in-law.

33. Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and the time a patrol car radios that it has arrived at the scene. Over a long period of time, it has been determined that the police response time has a normal distribution with a mean of 6.8 minutes and a standard deviation of 1.9 minutes. For a randomly received emergency call, find the following probabilities. (Round your answers to four decimal places.)

(a) the response time is between 3 and 8 minutes

(b) the response time is less than 3 minutes

(c) the response time is more than 8 minutes