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A clothing store asserts that 60% of its customers pay by credit. On a particular day, 35 customers purchased items at the store. a. What is the mean and standard deviation of the binomial distribution? b.What is the probability that half (18 or more) of the customers paid by credit? c. What is the probability that 30 or more paid by credit? d.What is the probability that less than 12 paid by credit? e. What is the probability that 12 to 30 paid by credit?

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Based on the percentage of customers that pay by credit and the number of customers that purchased, the following are true:

  1. Mean = 21; Standard deviation = 2.8983
  2. 0.8508
  3. 0.0009
  4. 0.0009
  5. 0.9982

What are the standard deviation and mean?

Mean is:

= 35 x 60%

= 21

Standard deviation:

= √(35 x 0.6 x (1-0.6)

= 2.8983

What are the probabilities for the clothing store?

Probability that half of customers paid by credit:

First, find the z value to use the Standard Normal Cumulative Probability table:

= (18 - 21) / 2.8983

= -1.04

= 1 - P(z < -1.04)

= 1 - 0.1492

= 0.8508

Probability that 30 or more paid by credit:

= (30 - 21) / 2.8983

= 3.11

= 1 - P (z < 3.11)

= 1 - 0.9991

= 0.0009

Probability that less than 12 paid by credit:

= (12 - 21) / 2.8983

= -3.11

= P (z ≤ -3.11)

= 0.0009

Probability that 12 to 30 paid by credit:

= P (12 ≤ x ≤ 30)

= P (-3.11 ≤ z ≤ 3.11)

= 0.9991 - 0.0009

= 0.9982

Find out more on the Standard Normal Cumulative Probability distribution at https://brainly.com/question/7207785.

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