General revision (Q1) State whether the following statements are true or false and give a brief explanation If the value of the linear correlation

Calculate the correlation between the student's grade in math and economics. What its type and strength.

Question (7):

   In a study of the relation between the expanding budget of advertisement on a specific product (X) in thousand of pounds and the quantity sold (Y), in tons, of a product. A sample of the advertising budget and the quantity sold in eight successive months is drawn from on of the companies which are dealing in such a product and the following information is obtained.

Using the previous information calculate

1)  The correlation coefficient (r) and the determinant coefficient ( ). Comment on the result.

2)  Find the regression line of Y on X and interpret the meaning of its intercept and regression coefficient.

3)    Predict the number of tones sold from this product if the expended advertising                   budget in one month is 25 thousand pounds.

Question (8):

   The food and drug administration (FDA) approves 20% of drugs submitted for its approval. In a random sample of 15 drugs submitted for the FDA's approval.

Find the probability that the number of drugs that are approved is at most three.

What is the mean and the standard deviation of the number of drugs submitted for the FDA's approval?

If the sample size of drugs is changed to be 30 drugs, what is the probability that the number of drugs that are approved is between 15 and 25 drugs?

Question (9):

The balances of all saving accounts at a local bank have a normal distribution with its mean equal to $ 12450 and standard deviation equal to $ 4160. Find the probability that the mean of a sample of 50 saving accounts selected from this bank will be

More than $ 11500.

Within $ 1500 of the population mean.

Find the number of accounts which will have an account of more than the population mean by at least $ 1000.

Question (10):

     Fast Auto service provides oil and lube for cars. It is known that the mean time taken for oil and lube service at this garage is 15 minutes per car with a standard deviation of 2.4 minutes. The management wants to promote the business guaranteeing a maximum waiting time for customers. If a customer's car is not served with that period, the customers will receive a 50% discount on the charge. The company wants to limit this discount to at most 5% of the customers. What should the maximum guaranteed waiting time be? Assume that the times taken for oil and lube service for all cars have a normal distribution.

Question (11):

   In a study of the relation between the experience (in years) (x) and the number of computers sold (y) during the last three months, we draw a sample of seven sales persons and obtain the following results

      The correlation coefficient ( r ) = 0.89

      Find:

Find the suitable least squares regression line.

Give a brief interpretation of the values of the Y-intercept and slope calculated in the previous part.

Calculate the determinant coefficient and interpret its value.

Predict the number of computers sold during the past three months by salespersons with twenty years experience.