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QuestionFind the z-scores for vacation expenses of \$ 197, \$ 277, and \$ 310, given average \$ 247 and SD \$ 60.

Studdy Solution

STEP 1

Assumptions1. The average daily expense for food and lodging is \$247. The standard deviation of the daily expense is \$603. The data follows a normal distribution4. We need to find the z-scores for daily expenses of \$197, \$277, and \$310

STEP 2

The z-score is a measure of how many standard deviations an element is from the mean. It can be calculated using the following formulaz=X−μσz = \frac{X - \mu}{\sigma}where- zz is the z-score, - XX is the value for which we want to find the z-score, - μ\mu is the mean of the data, - σ\sigma is the standard deviation of the data.

STEP 3

Let's calculate the z-score for a daily expense of \$197.
Plug in the values for XX, μ\mu, and σ\sigma into the z-score formulaz=$197−$247$60z = \frac{\$197 - \$247}{\$60}

STEP 4

Calculate the z-score for a daily expense of \$197.
z=$197−$247$60=−0.83z = \frac{\$197 - \$247}{\$60} = -0.83

STEP 5

Now, let's calculate the z-score for a daily expense of \$277.
Plug in the values for XX, μ\mu, and σ\sigma into the z-score formulaz=$277−$247$60z = \frac{\$277 - \$247}{\$60}

STEP 6

Calculate the z-score for a daily expense of \$277.
z=$277−$247$60=0.50z = \frac{\$277 - \$247}{\$60} =0.50

STEP 7

Finally, let's calculate the z-score for a daily expense of \$310.
Plug in the values for XX, μ\mu, and σ\sigma into the z-score formulaz=$310−$247$60z = \frac{\$310 - \$247}{\$60}

STEP 8

Calculate the z-score for a daily expense of \$310.
z=$310−$247$60=1.05z = \frac{\$310 - \$247}{\$60} =1.05So, the z-scores for the daily expenses of \$197, \$277, and \$310 are -0.83,0.50, and1.05 respectively.

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