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Chapter 7: Q. 56 (page 430)

A uniform distribution has a minimum of six and a maximum of ten. A sample of 50is taken.

Find the 90th percentile for the sums.

Short Answer

Expert verified

The 90th percentile for the sum is410.4512.

Step by step solution

01

Given Information

Given a sample of 50 variables with uniform distribution U(6,10).

02

Calculation

If variable Zhas a uniform distribution on the interval [6,10], then the mean of Zis 8and the standard deviation is 1.1547.

Thus the allocation of the sums is:

N(50路8,50路1.1547)=N(400,8.165)

Finding the 90th percentile:

P(危x<z)=0.9

P危x-4008.165<z-4008.165=0.9

If variable Zhas a standard normal distribution, then

P(Z<1.28)=0.9

Thus,

z-4008.165=1.28

z-400=10.4512

z=410.4512.

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