3 years ago

31 points!

Mathematics

1 answer:

AlekseyPX3 years ago

6 0

Answer:

Step-by-step explanation:

show me the problem and make me brainliest

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A courier service company wishes to estimate the proportion of people in various states that will use its services. Suppose the

Svetradugi [14.3K]

Answer:

The probability that the sample proportion will be less than 0.05 is 0.80511.

Step-by-step explanation:

We are given that a courier service company wishes to estimate the proportion of people in various states that will use its services.

Suppose the true proportion is 0.04 and 349 are sampled.

Let $\hat p$ = sample proportion

The z score probability distribution for sample proportion is given by;

Z = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion

n = sample size = 349

p = population proportion = 0.04

Now, the probability that the sample proportion will be less than 0.05 is given by = P( $\hat p$ < 0.05)

P( $\hat p$ < 0.05) = P( $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < $\frac{0.05-0.04}{\sqrt{\frac{0.05(1-0.05)}{349} } }$ ) = P(Z < 0.86) = 0.80511

The above probability is calculated by looking at the value of x = 0.86 from the z table which has an area of 0.80511.

Hence, the probability that the sample proportion will be less than 0.05 is 0.80511.

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