# Sampling Probability Distribution

The Food Marketing Institute shows that 17% of households spend more than $100 per week on groceries. Assume that the population proportion is 0.17.

a. If a random sample of 800 households is selected from the population, what is the probability that the sample proportion will be between 0.15 and 0.19?

b. If a random sample of 1600 households is selected from the population, what is the probability that the sample proportion will be between 0.15 and 0.19?

c. If a random sample of 1000 households is selected from the population, what is the probability that the sample proportion will be less than 0.18?

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#### Solution Preview

a) Standard Error =(p*q/n)^0.5=(0.17*0.83/800)^0.5=0.013280625

z=(p-P bar)/Standard error

For 0.15, we have z= (0.15-0.17)/0.0133=-1.50

For 0.19, we have z= ...

#### Solution Summary

The expert examines sampling probably for distribution.