Question

An airliner carries 200 passengers and has doors with a height of 76 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 The probability is (Round to four decimal places as needed.) b. If half of the 200 passengers are men find the probability that the mean height of the 100 men is less than 76 in The probability is (Round to four decimal places as needed.) c. When considering the comfort and safety of passengers, which result is more relevant the probability from part(a) or the probability from part (1) Why? OA. The probability from part(a) is more relevant because it shows the proportion of flights where the mean height of the male passengers will be less than the door height OB. The probability from part (a) is more relevant because it shows the proportion of male passengers that will not need to bend O C. The probability from part(b) is more relevant because it shows the proportion of male passengers that will not need to bend D. The probability from part(b) is more relevant because it shows the proportion of fights where the mean height of the male passengers will be less than the

Answer 1

a) Given = b) Givena Given = c) Option D d) Option A = 69 = 0.2800 y = 69 = 2.8 Ha 69 o = 3 n = 100 P(less than 76)= P(less than 76) PIX76)= PIX<76)= Now, According to central limit theorem.... = P(X-/ 0 76-1/o) = P(X-4/ 0<76-/o) x = (69,0.28) = P(Z<76-69/0.28) = PIZ<76-69/2.8) HX = = 69 o = 0.2800 = P(Z<25) = P(Z<2.5) .....where,o = 2.8/100 = 1.0000 = 0.9938 .....(from standard normal distribution table) .....(from standard normal distribution table)

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