Mathematics, 07.06.2020 05:57 heids17043

A recent study reported that 28% of shoppers only review one page when searching online for product information. A random sample of 100 shoppers was randomly selected. What is the probability that between 20 and 30 of these shoppers only review one page when searching online?

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Answer from: thomasmurphy200

68.29% probability that between 20 and 30 of these shoppers only review one page when searching online

Step-by-step explanation:

I am going to use the normal approximation to the binomial to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

n = 100, p = 0.28

$\mu = E(X) = np = 100*0.28 = 28$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.28*0.72} = 4.49$

What is the probability that between 20 and 30 of these shoppers only review one page when searching online?

Using continuity correction, this is $P(20 - 0.5 \leq X \leq 30 + 0.5) = P(19.5 \leq X \leq 30.5)$ , which is the pvalue of Z when X = 30.5 subtracted by the pvalue of Z when X = 19.5.

X = 30.5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{30.5 - 28}{4.49}$

Z = 0.56

Z = 0.56 has a pvalue of 0.7123.

X = 19.5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{19.5 - 28}{4.49}$

Z = -1.89

Z = -1.89 has a pvalue of 0.0294

0.7123 - 0.0294 = 0.6829

68.29% probability that between 20 and 30 of these shoppers only review one page when searching online

Answer from: Quest

16.9 times 2.85

step-by-step explanation:

Answer from: Quest

image result for what is another name for consecutive interior angles?

when two lines are crossed by another line (called the transversal): the pairs of angles on one side of the transversal but inside the two lines are called consecutive interior angles. in this example, these are consecutive interior angles: d and f.

step-by-step explanation:

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