Question

The heights of children are normally distributed. For three year old girls, the mean height is 38.7 inches and the standard deviation is 3.2 inches. A random sample of 14 three year old girls are chosen. Find P(x⎯⎯⎯ < 37) for n = 14. Enter your answer as an area under the curve with 4 decimal places.

Answer 1

Solution :

Given that,

mean = = 38.7

standard deviation = = 3.2

n = 14

= 38.7

=  / n = 3.2 / 14=0.8552

P( < 37) = P[( - ) / < (37-38.7) / 0.8552]

= P(z <-1.99 )

Using z table  

= 0.0233   

probability= 0.0233