Question

The Grocery Manufacturers of America reported that 76% of consumers read the ingredients listed on a product's label. Assume a simple random sample of 400 customers is selected from the population.

1. What conditions are met? Confirm independence of the sample with two conditions and confirm that the normal model is appropriate with a sample size condition.

2. What is the model for the sampling distribution?

3. What is the probability that the sample proportion will be less than 70%?

Answer 1

p = 0.76

n = 400

1)

n*p = 400*0.76 = 304 > 10

n*(1-p) = 400*0.24 = 96 > 10

Both are greater than 10 so we can use normal model.

2)

The sample proportion follows normal distribution with

mean = = p = 0.76

And standard deviation is

3)

We have to find P( < 0.70)

For finding this probability we have to find z score.

That is we have to find P(Z < - 2.81)

P(Z < - 2.81) = 0.0025

( From z table)

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