Question

an airliner carries 50 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 2.8in

what is the probability?

if half of 50 passengers are, find the probability that the mean height of the 25 men is less than 74in

Answer 1

Solution :

Given that ,

mean = = 69.0

standard deviation = = 2.8

1) n = 50

=   = 69.0

= / n = 2.8 / 50 = 0.40

P( < 74) = P(( - ) / < (74 - 69.0) / 2.8)

= P(z < 1.79)

Using z table

= 0.9633

2) n = 25

=   = 69.0

= / n = 2.8 / 25 = 0.56

P( < 74) = P(( - ) / < (74 - 69.0) / 0.56)

= P(z < 8.93)

Using z table

= 1