Question

use the normal distribution to approximate the following binomial distribution: a convenience store owner claims that 55% of the people buying from her store, on a certain day of the week, buy coffee during their visit. a random sample of 35 customers is made. if the store owner's claim is correct, what is the probability that fewer than 20 customers in the sample buy coffee during their visit on that certain day of the week? a) exam image b) exam image c) exam image d) exam image e) exam image f) none of the above.

Answer 1

The probability that fewer than 20 customers in the sample buy coffee during their visit on that certain day of the week is 59.87%

What is the normal distribution?

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.

The formula for z-score is z = (x -μ)/σ

Where,

Z is standard score.

X is observed value.

μ is mean of the sample.

σ is standard deviation of the sample

Given that 55% of the customers buy coffee, hence p = 55% = 0.55

Sample of 35 customers, hence n = 35.

For the normal distribution μ = np, σ = √[np(1-p)]

The mean and the standard deviation of the approximation are:

μ = 35 ˣ 0.55 = 19.25

σ = √[35 ˣ 0.55(1-0.55)] =2.943

Using continuity correction, the probability that fewer than 20 customers in the sample buy coffee during their visit on that certain day of the week is P(X < 20 - 0.5) = P(X < 19.5), which is the p-value of Z when X = 19.5, hence:

z = (20 -19.25)/2.943

z = 0.25 has a p-value of 0.5987.

0.5987 =59.87%

To learn more about binomial distribution, click on below link

https://brainly.com/question/16184408

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