Question

1/The heights of adult men in America are normally distributed, with a mean of 69.2 inches and a standard deviation of 2.65 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.5 inches and a standard deviation of 2.51 inches.
a) If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)?
z =
b) What percentage of men are SHORTER than 6 feet 3 inches? Round to nearest tenth of a percent.
%
c) If a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)?
z =
d) What percentage of women are TALLER than 5 feet 11 inches? Round to nearest tenth of a percent.
e) Who is relatively taller: a 6'3" American man or a 5'11" American woman? Defend your choice in a meaningful sentence.

Suppose that about 84% of graduating students attend their graduation. A group of 35 students is randomly chosen, and let X be the number of students who attended their graduation.

Please show the following answers to 4 decimal places.

1. What is the distribution of X? X ~ ? B U N  (,)
2. What is the probability that exactly 25 number of students who attended their graduation in this study?
3. What is the probability that less than 25 number of students who attended their graduation in this study?
4. What is the probability that at least 25 number of students who attended their graduation in this study?
5. What is the probability that between 22 and 26 (including 22 and 26) number of students who attended their graduation in this study?
6. 3/According to the American Red Cross, 11% of all Connecticut residents have Type B blood. A random sample of 20 Connecticut residents is taken.

   X=X=the number of CT residents that have Type B blood, of the 20 sampled.
   What is the expected value of the random variable XX?
   2.28 2.26 2.04 2.2 1.9 2.08

7. 4/The owner of a small deli is trying to decide whether to discontinue selling magazines. He suspects that only 10.7% of his customers buy a magazine and he thinks that he might be able to use the display space to sell something more profitable. Before making a final decision, he decides that for one day he will keep track of the number of customers that buy a magazine. Assuming his suspicion that 10.7% of his customers buy a magazine is correct, what is the probability that exactly 6 out of the first 12 customers buy a magazine?

Answer 1