Stats question 1. ____________________________________ 2. (b) The probability for (b) above is (rounded to 4 places) 3.) ) (b) If 10 women are randomly selected, find the probability that they have a mean height between 63.2 in and 64.2 in. (c) Why can the central limit theorem be used in part (b), even though the sample size does not exceed 30? The central limit theorem can be used in two different cases, when the sample size is large and when the population is normally distributed. Carefully read the problem to identify the reason that the theorem can be used in this case. 4.) answer a,b,c b. hint for b In this case, the desired probability is for the mean of a sample of 60 times. Therefore, use the central limit theorem. 5. The capacity of an elevator is 15 people or 2490 pounds. The capacity will be exceeded if 15 people have weights with a mean greater than 2490 divided by 15 equals 166 pounds.2490/15=166 pounds. Suppose the people have weights that are normally distributed with a mean of 172 lb and a standard deviation of 31 lb. a. Find the probability that if a person is randomly selected, his weight will be greater than 166 pounds. The probability is approximately ? (round to 4 places) b. Find the probability that 15 randomly selected people will have a mean that is greater than 165 pounds.In this case, the desired probability is for the mean of a sample of 15 people. Therefore, use the central limit theorem. c. Does the elevator appear to have the correct weight limit? Why or why not? If the weight limit is correct, then the operator would not have to be concerned about the weight of the people on the elevator. He would simply need to ensure that the number of people does not exceed the stated capacity. Use the probability that the mean of 15 randomly selected people is greater than 165 to determine if this is a reasonable assumption. 6. Based on a survey, for women aged 18 to 24, systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.8 and a standard deviation of 13.2. Complete parts (a) through (d). a. If a woman between the ages of 18 and 24 is randomly selected, find the probability that her systolic blood pressure is greater than 120. b. If 4 women in that age bracket are randomly selected, find the probability that their mean systolic blood pressure is greater than 120. c. Given that part (b) involves a sample size that is not larger than 30, why can the central limit theorem be used? Use information from below. d. If a physician is given a report stating that 4 women have a mean systolic blood pressure below 120, can she conclude that none of the women have a blood pressure greater than 120? Why? Use this information to determine if the physician can conclude that none of the women have a blood pressure greater than 120. 7. An airliner carries 400 passengers and has doors with a height of 74 in. Heights of men are normally distributed with a mean of 69.0 in and a standard deviation of 2.8 in. Complete parts (a) through (d). a. If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending. b. If half of the 400 passengers are men, find the probability that the mean height of the 200 men is less than 74 in. c. When considering the comfort and safety of passengers, which result is more relevant: the probability from part (a) or the probability from part (b)? Why? d. When considering the comfort and safety of passengers, why are women ignored in this case? First consider the difference in height, in general, between men and women. Then decide whether this difference constitutes adequate grounds for ignoring women. 8. An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 150 lb and 191 lb. The new population of pilots has normally distributed weights with a mean of 158 lb and a standard deviation of 25.4 lb. a. If a pilot is randomly selected, find the probability that his weight is between 150 lb and 191 lb b. If 32 different pilots are randomly selected, find the probability that their mean weight is between 150 lb and 191 lb.In this case, the desired probability is for the mean of a sample of 32 pilots. Therefore, use the central limit theorem. List mean probability for samples of 30,31,32,33,34,35,36,37,38,39,40 c. When redesigning the ejection seat, which probability is more relevant? 9. Suppose certain coins have weights that are normally distributed with a mean of 5.309 g and a standard deviation of 0.077 g. A vending machine is configured to accept those coins with weights between 5.229 g and 5.389 g. a. If 280 different coins are inserted into the vending machine, what is the expected number of rejected coins? The expected number of rejected coins is _____ (round to nearest integer) b. If 280 different coins are inserted into the vending machine, what is the probability that the mean falls between the limits of 5.229 g and 5.389 g? c. Which results is more important to the owner of the vending machine? Why? 10. Cans of a certain beverage are labeled to indicate that they contain 12 oz. The amounts in a sample of cans are measured and the sample statistics are n=45 and x=12.01 oz. If the beverage cans are filled so that =12.00 oz (as labeled) and the population standard deviation is =0.093 oz (based on the sample results), find the probability that a sample of 45 cans will have a mean of 12.01 oz or greater. Do these results suggest that the beverage cans are filled with an amount greater than 12.00 oz? a.) the probability that a sample of 45 cans will have a mean of 12.01 oz or greater, given that =12.00 and sigma equals =0.093, is B Do these results suggest that the beverage cans are filled with an amount greater than 12.00 oz? (hint:The rare event rule for inferential statistics states that if, under a given assumption, the probability of a particular observed event is exceptionally small (such as less than 0.05), then conclude that the assumption is probably not correct.)