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The number of customers that come to a certain clothing store each day follows a normal distribution. The mean number of customers is 428, and the standard deviation is 32. What is the probability that more than 524 customers will come to the store on a given day?

A.
0.15%
B.
0.3%
C.
2.5%
D.
5%

Respuesta :

Answer: the true answer is A

Step-by-step explanation:

Good luck, give Brainliest

Using the normal distribution, it is found that the probability that more than 524 customers will come to the store on a given day is given by:

A. 0.15%.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

  • The z-score measures how many standard deviations the measure is above or below the mean.
  • Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

In this problem, the mean and the standard deviation are given, respectively, by:

[tex]\mu = 428, \sigma = 32[/tex].

The probability that more than 524 customers will come to the store on a given day is one subtracted by the p-value of Z when X = 524, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{524 - 428}{32}[/tex]

Z = 3

Z = 3 has a p-value of 0.9985.

1 - 0.9985 = 0.0015 = 0.15%.

Hence option A is correct.

More can be learned about the normal distribution at https://brainly.com/question/24663213

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