Question

Goofy's fast food center wishes to estimate the proportion of people in its city that will purchase its products. Suppose the true proportion is 0.07. If 313 are sampled, what is the probability that the sample proportion will be less than 0.04

Answer 1

The probability that the sample proportion will be less than 0.04 is 0.0188 or 1.88%.

The true proportion given to us (p) = 0.07.

The sample size is given to us (n) = 313.

The standard deviation can be calculated as (s) = √[{p(1 - p)}/n] = √[{0.07(1 - 0.07)}/313] = √{0.07*0.93/313} = √0.000207987 = 0.0144217.

The mean (μ) = p = 0.07.

Since np = 12.52 and n(1 - p) = 291.09 are both greater than 5, the sample is normally distributed.

We are asked the probability that the sample proportion will be less than 0.04.

Using normal distribution, this can be shown as:

P(X < 0.04),

= P(Z < {(0.04-0.07)/0.0144217}) {Using the formula Z = (x - μ)/s},

= P(Z < -2.0802)

= 0.0188 or 1.88% {From table}.

Thus, the probability that the sample proportion will be less than 0.04 is 0.0188 or 1.88%.

Learn more about the probability of sampling distributions at

brainly.com/question/15520013

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