Question

A Food Marketing Institute found that 30% of households spend more than $125 a week on groceries. Assume the population proportion is 0.3 and a simple random sample of 187 households is selected from the population. What is the probability that the sample proportion of households spending more than $125 a week is less than 0.27?

Note: You should carefully round any intermediate values you calculate to 4 decimal places to match wamap's approach and calculations.

Answer =  (Enter your answer as a number accurate to 4 decimal places.)

Answer 1

A Food Marketing Institute found that 30% of households spend more than $125 a week on groceries.

Population proportion, p = 0.30

simple random sample, n = 187

To calculate: The probability that the sample proportion of households spending more than $125 a week is less than 0.27.

Now,

Since sample size is larger than 30 we can assume normality of population proportion.

By using central limit theorem

Therefore the probability that the sample proportion of households spending more than $125 a week is less than 0.27 is 0.1841