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In-s [12.5K]
3 years ago
5

Berdine's Chicken Factory has several stores in the Hilton Head, South Carolina, area. When interviewing applicants for server p

ositions, the owner would like to include information on the amount of tip a server can expect to earn per check (or bill). A study of 500 recent checks indicated the server earned the following amounts in tips per 8-hour shift.Amount of tip Number0-20 20020-50 10050-100 75100-200 75more than 200 50total 500what is the probability of a tim 200 or more?
Mathematics
1 answer:
nata0808 [166]3 years ago
5 0

Answer:

The probability of the tip to be more than 200 is 0.1.

Step-by-step explanation:

As per the given data

Amount of tip            Number

     0-20                       200

   20-50                       100

   50-100                      75

 100-200                     75

    200+                        50

____________________

Total=                         500

So what is the probability of tip to be more than 200 is given as

P(200+)=\frac{no. \, of\,occurrence}{Total\, Number}

From the table the value is 50 for the tip to be more than 200 where as the total occurrences are 500 so substituting values:

P(200+)=\frac{no. \, of\,occurrence}{Total\, Number}\\P(200+)=\frac{50}{500}\\P(200+)=0.1

So the probability of the tip to be more than 200 is 0.1.

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Assume that blood pressure readings are normally distributed with a mean of 115 and a standard deviation of 8. If 100 people are
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D. 0.9938.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

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In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

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The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

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For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 115 and a standard deviation of 8.

This means that \mu = 115, \sigma = 8

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This means that n = 100, s = \frac{8}{\sqrt{100}} = 0.8

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This is the p-value of Z when X = 117, so:

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

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Z = \frac{117 - 115}{0.8}

Z = 2.5

Z = 2.5 has a p-value of 0.9938, and thus, the correct answer is given by option D.

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3 years ago
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