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natta225 [31]
3 years ago
11

The five employees at a store are each paid $5.50, $6, $10, $6.50, and $6 per hour respectively. When one of the employees being

paid $6 asks his boss for a raise, which measure of central tendency will BEST support his request to be paid more?
Mathematics
1 answer:
Kryger [21]3 years ago
8 0

Answer:

Mean

Step-by-step explanation:

The most common measures of central tendency are mode, median and mean.

The mode of the data set is the value that is repeated the most. In this case, the mode is $6 (appears twice), which does not support the raise claim of the employee.

The median is the central value of the data set. In this case, the median is also $6 (third highest value), which does not support the raise claim of the employee.

The mean of the salaries is:

m=\frac{5.50+6+10+6.50+6}{5}\\m=\$6.80

Since the mean is greater than the employee's current wage, it would best support his request to be paid more.

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d1i1m1o1n [39]

Answer:

a) 96.64% probability that maximum speed is at most 50 km/h

b) 24.67% probability that maximum speed is at least 48 km/h

c) 86.64% probability that maximum speed differs from the mean value by at most 1.5 standard deviations

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

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

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

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 pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\mu = 46.8, \sigma = 1.75

A. What is the probability that maximum speed is at most 50 km/h?

This is the pvalue of Z when X = 50. So

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

Z = \frac{50 - 46.8}{1.75}

Z = 1.83

Z = 1.83 has a pvalue of 0.9664

96.64% probability that maximum speed is at most 50 km/h.

B. What is the probability that maximum speed is at least 48 km/h?

This is 1 subtracted by the pvalue of Z when X = 48.

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

Z = \frac{48 - 46.8}{1.75}

Z = 0.685

Z = 0.685 has a pvalue of 0.7533

1 - 0.7533 = 0.2467

24.67% probability that maximum speed is at least 48 km/h.

C. What is the probability that maximum speed differs from the mean value by at most 1.5 standard deviations?

Z = 1.5 has a pvalue of 0.9332

Z = -1.5 has a pvalue of 0.0668

0.9332 - 0.0668 = 0.8664

86.64% probability that maximum speed differs from the mean value by at most 1.5 standard deviations

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Step-by-step explanation:

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