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# A casino game works as follows: A player pays $1 to play. Then, the player draws a card randomly from a standard playing deck. If the card is an ace,...

c) If 1001 cedar logs arriving at the mill from Part (a) are randomly selected, what is the probability that exactly half of them will be suitable for timber framing?

5. In a plantation of sunflowers, the height of plants tends to follow a normal distribution, with a mean of 2.86 m and a standard deviation of 0.37 m.

a) What is the probability that a randomly- selected sunflower measures exactly 3.00 m in height?

b) What is the probability that a randomly-selected sunflower measures 3.00 m in height, using a measuring stick that is precise to the nearest cm ?

c) Calculate, to the nearest %, the proportion of sunflowers that are shorter than 200 cm in height.

d) Calculate, to the nearest %, the probability that a randomly-selected sunflower from this plantation has a height between 200 and 286 cm.

e) It has been decided that the tallest 3% of sunflowers in the plantation are to be set aside for seed-saving. Calculate to the nearest cm, the minimum height for a sunflower to be saved for seeds.

f) A certain species of crawling insect is known to favour the roots of the variety of sunflower grown in this plantation. If 8 of these insects arrive in the plantation and each one selects a different sunflower, and it is assumed that they are unable to discern the heights of the plants from their position on the ground, then what is the probability, to the nearest %, that less than half of these insects will choose a sunflower with a height between 200 and 286 cm?

6. The mass of garbage put out for weekly curtsied pickup, per household, in a certain community, is reported to have a mean of 6.1 kg and a standard deviation of 2.2 kg. Based on this information:

a) Assume that the population is very large. For a sample of 100 households from this community, calculate, to the nearest %, the probability that the sample mean will be between 5.9 and 6.3 kg.

b) Redo part (a), for a sample size of 1000 households instead of 100.

c) Redo part (a), (i.e., n=100), but this time assume a population of 400 households.

d) Assuming again that the population is very large, let us now suppose that 5 consecutive samples of 100 households are taken, and each one of them has a sample mean greater than 6.6 kg. Calculate the probability of obtaining this result.

e) Based on your answer for Part (d), is there reason to believe that the mean weekly garbage output per household is not actually around 6.1kg? If so, in which direction has the mean garbage output shifted? Explain your answers using your previous calculations for this question, plus your knowledge of statistics fundamentals.

7. Based upon historical data, the successful seed germination fate for a certain variety of lettuce is 31%. A plant nursery has recently sowed 10000 of these seeds, and then shortly after received orders for lettuce plants that can only be filled from successful germinations from this sowing.

a) If the order is for 3000 lettuce plants, what is the probability that they can fill all of these orders?

b) Redo Part (a) for an order of 3300 lettuce plants.

c) Failing to deliver on orders is somewhat that cannot be 1005 avoided in this line of work. However, one can decide on a maximum acceptable level of risk of this failure occurring. If this particular nursery is willing to accept a risk of such failure occurring. If this particular nursery is willing to accept a risk of such failures - i.e., of not having enough germinated plants from a sowing to meet all orders - of up to but not exceeding 5%, then what is the largest total amount of plants it should take orders for, for each sowing of 10000 of these seeds?