Question

The height of all adult females in Georgia is normally distributed with a mean height of 67.4 inches and a standard deviation of 2.8 inches. A random sample of 4 females from Georgia are selected. What is the probability the mean height of the 4 females is greater than 68.4 inches?

Do not round any values until you get to your final answer. Round your final answer to three decimals of accuracy (e.g. 0.08493 would round to 0.085)

Your Answer:

Answer 1

Solution :

Given that,

mean = = 67.4

standard deviation = =2.8

n=4

= =67.4

= / n = 2.8/ 4 = 1.4

P( >68.4 ) = 1 - P( < 68.4)

= 1 - P[( - ) / < (68.4 - 67.4) /1.4 ]

= 1 - P(z <0.71 )

Using z table

= 1 - 0.7611

probability=  0.2389=0.239