The overhead reach distances of adult females are normally distributed with a mean of 195cm and a standard deviation of 8.3cm.

a. Find the probability that an individual distance is greater than 208.40 cm.

b. Find the probability that the mean for 20

randomly selected distances is greater than 193.50cm.

c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?

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Part 1

a. The probability-- - -is enter your response here.

(Round to four decimal places as needed.)

2- An airliner carries 150 passengers and has doors with a height of 75 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).

. 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.)

Part 2b. If half of the 150 passengers are men, find the probability that the mean height of the 75 men is less than 75

in.The probability is

enter your response here.

(Round to four decimal places as needed.)