Question

Consider the approximately normal population of heights of male college students with mean μ = 68 inches and standard deviation of σ = 4.6 inches. A random sample of 13 heights is obtained.

(b) Find the proportion of male college students whose height is greater than 71 inches. (Round your answer to four decimal places.)
e) Find P(x > 71). (Round your answer to four decimal places.)
(f) Find P(x < 70). (Round your answer to four decimal places.)

Answer 1

Solution :

Given that,

mean = = 68

standard deviation = = 4.6

a ) P (x > 71 )

= 1 - P (x < 71 )

= 1 - P ( x -  / ) < ( 71 - 68 / 4.6)

= 1 - P ( z < 3 / 4.6)

= 1 - P ( z < 0.65 )

Using z table

= 1 - 0.7422

= 0.2578

Probability = 0.2578

b ) P( x < 70 )

P ( x - / ) < ( 70 - 68 / 4.6)

P ( z < 2 / 4.6 )

P ( z < 0.43)

= 0.6664

Probability =0.6664