Question

use the appropriate normal distribution to approximate the resulting binomial distributions. 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 21 customers in the sample buy coffee during their visit on that certain day of the week? a) 0.7486 b) 0.6915 c) 0.7224 d) 0.5987 e) 0.6628 f) none of the above.

Answer 1

The probability that fewer than 21 customers in the sample buy coffee during their visit on that certain day of the week is 0.7224. Hence option C is the correct option.

What is the binomial distribution?

When each trial has the same probability of achieving a given value, the number of trials or observations is summarised using the binomial distribution. The likelihood of observing a specific number of successful outcomes in a specific number of trials is determined by the binomial distribution.

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

Where, 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 binomial 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

Now calculate the z score where μ = 19.25, σ = 2.943 and X = 21

z = (21 -19.25)/2.943

z = 0.59

The value of p is 0.2776 when z score is 0.59.

The probability is 1 - 0.2776 = 0.7224.

To learn more about normal distribution, click on below link

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