Question

Probability and Statistics Test Time: 40 mins #1. The Swedish population of men's heights is approximately normally distributed with a mean of 69 inches and standard deviation of 3 inches. If a Swedish man is chosen at random: (a) What is the probability that he is under 5 feet (60 inches)? (b) What is the probability that he is between 5 feet (60 inches) and 6 feet (72 inches)? (c) What height is exceeded by 25% of the men? (d) If 20 men are selected at random what is the probability that their mean height is greater than 70 inches? (e) If the heights of the men are not normally distributed which of the answers (a) to (d) are valid. Explain your reasoning. #2. From many years of observation, a biologist knows the probability is only 0.65 that any given Arctic tern will survive the migration from its summer nesting area to its winter feeding grounds. A random sample of 500 Arctic terns were banded at their summer nesting area. Use the normal approximation to the binomial to find the probability that more than 300 of the banded Arctic terns will survive the migration. Given that the mean and variance of a binomial distribution are as follows: #3. Four runners, Andy, Bob, Chris and Dai, train to take part in a 1600m relay race, in which Andy is to run 100m, Bob 200m, Chris 500m and Dai 800m. During training their individual times, recorded in seconds, follow normal distributions. With obvious notation, these are: Find the probability that they run the relay race in less than 3 minutes 35 seconds.

Answer 1

olution :- 0.003 Z < 3. le=69 5=3 a) P(x260)=P(22 60-69) = Plze-3) (0.00137 by P (60 2 XL 72) = P | 60-69 (2L 72-69) = P(-32221) 0.8400 Z-score for 25th percentile = -0.67 2=8-11 =) - 0.67= *-69 = x=567 d) P(+370) = P17>70-69) = P1231.49) 10-0681 e) No I population is not normally distributed we connot apply these, so these will be not valid X l