Question

Suppose the heights of 18-year-old men are approximately normally distributed, with mean 68 inches and standard deviation 3inches.

(a) What is the probability that an 18-year-old man selected at random is between 67 and 69 inches tall? (Round your answer to four decimal places.)


(b) If a random sample of eleven 18-year-old men is selected, what is the probability that the mean height x is between 67 and 69 inches? (Round your answer to four decimal places.)

Answer 1

Solution :

Given that ,

mean = = 68

standard deviation = = 3

(A)P(67< x <69 ) = P[(67 - 68) /3 < (x - ) / < (69 - 68) /3 )]

= P( -0.33< Z <0.33 )

= P(Z < 0.33) - P(Z <-0.33 )

Using z table,  

=0.6293 -0.3707

= 0.2586

(B)

n = 11

= 68

=  / n = 3 / 11=0.9045

P(67<   <69 ) = P[(67 - 68) / 0.9045< ( - ) /   < (69 - 68) 0.9045/ )]

= P( -1.11< Z <1.11 )

= P(Z <1.11 ) - P(Z <-1.11 )

Using z table,  

=0.8665 -0.1335

=0.7320