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Studentka2010 [4]
1 year ago
13

4. (40 Pts) The Vacation Times website rates recreational vehicle campgrounds

Mathematics
1 answer:
dusya [7]1 year ago
6 0

Using the normal distribution, it is found that:

a) The rating would have to be of at least 9.78.

b) The z-score for a rating of 5 is of -1.53.

<h3>Normal Probability Distribution</h3>

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

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

  • 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.

The mean and the standard deviation are given by:

\mu = 7.6, \sigma = 1.7

For item a, we have to find the 90th percentile, which is <u>X when Z = 1.28</u>, hence:

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

1.28 = (X - 7.6)/1.7

X - 7.6 = 1.28 x 1.7

X = 9.78.

The rating would have to be of at least 9.78.

For item b, we have to find <u>Z when X = 5</u>, hence:

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

Z = (5 - 7.6)/1.7

Z = -1.53.


The z-score for a rating of 5 is of -1.53.

More can be learned about the normal distribution at brainly.com/question/24808124

#SPJ1

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