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In: Statistics and Probability

The heights of children are normally distributed. For three year old girls, the mean height is...

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)

Solutions

Expert Solution

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


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