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 5 three year old girls are chosen. Find P(x⎯⎯⎯ < 37) for n = 5. Enter your answer as an area under the curve with 4 decimal places. P(x⎯⎯⎯ < 37)

Answer 1

Solution :

Given that,

mean = = 38.7

standard deviation = = 3.2

n = 5

= 38.7

=  / n =3.2 / 5=1.43

P( < 37) = P[( - ) / < (37-38.7) /1.43 ]

= P(z < -1.19)

Using z table      

probability= 0.1170