/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 19 From Amazon.com, the prices of 1... [FREE SOLUTION] | 91影视

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Chapter 3: Problem 19

From Amazon.com, the prices of 10 varieties of orange juice \((59-\) to 64 -ounce containers) sold were recorded: \(\$ 3.88, \$ 2.99, \$ 3.99, \$ 2.99, \$ 3.69, \$ 2.99, \$ 4.49\), \(\$ 3.69, \$ 3.89, \$ 3.99 .\) a. Find and interpret the mean price of orange juice sold on this site. Round to the nearest cent. b. Find the standard deviation for the prices. Round to the nearest cent. Explain what this value means in the context of the data.

Short Answer

Expert verified
The mean price is the average price of orange juice sold on the site, important to understand a 鈥渢ypical鈥� price for the juice. The standard deviation shows the amount of variability or dispersion from this average price.

Step by step solution

01

Calculate Mean

To calculate the mean price, add together all the prices and divide by the total number of prices. So, the mean \( \mu \) is computed as \( \mu = \frac{1}{n} \sum_{i=1}^{n} x_i \), where \( x_i \) are the prices and \( n \) is the total number of prices.
02

Calculate Standard Deviation

The standard deviation \( \sigma \) is computed as \( \sigma = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (x_i - \mu)^2} \). In other words, subtract the mean from each price, square the result, then average these squared results. The square root of that average gives the standard deviation.
03

Interpret the Mean and Standard Deviation

The average, or mean price of orange juice gives an indication of what price a randomly selected orange juice would be expected to be sold at. A larger standard deviation would indicate a wide spread in prices, while a smaller one would suggest prices are relatively similar to the mean.

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Most popular questions from this chapter

Babies born after 40 weeks gestation have a mean length of \(52.2\) centimeters (about \(20.6\) inches). Babies born one month early have a mean length of \(47.4\) centimeters. Assume both standard deviations are \(2.5\) centimeters and the distributions are unimodal and symmetric. (Source: www.babycenter.com) a. Find the standardized score (z-score), relative to all U.S. births, for a baby with a birth length of 45 centimeters. b. Find the standardized score of a birth length of 45 centimeters for babies born one month early, using \(47.4\) as the mean. c. For which group is a birth length of 45 centimeters more common? Explain what that means.

Wedding Costs by Gender (Example 3) StatCrunch did a survey asking respondents their gender and how much they thought should be spent on a wedding. The following table shows Minitab descriptive statistics for wedding costs, split by gender. a. How many people were surveyed? b. Compare the results for men and women. Which group thought more should be spent on a wedding? Which group had more variation in their responses? Descriptive Statistics: Amount Statistics $$ \begin{array}{ccccccccc} & & & & \text { Mini- } & & & \text { Maxi- } \\ \text { Variable } & \text { Gender } & \mathbf{N} & \text { Mean } & \text { StDev } & \text { mum } & \text { Q1 } & \text { Median } & \text { Q3 } & \text { mum } \\ \hline \text { Amount } & \text { Female } & 117 & 35,378 & 132,479 & 0 & 5,000 & 10,000 & 20,000 & 1,000,000 \\ & \text { Male } & 68 & 54,072 & 139,105 & 2 & 5,000 & 10,000 & 30,000 & 809,957 \end{array} $$

Note: Reported interquartile ranges will vary depending on technology. Name two measures of the variation of a distribution, and state the conditions under which each measure is preferred for measuring the variability of a single data set.

Construct two sets of numbers with at least five numbers in each set with the following characteristics: The means are the same, but the standard deviation of one of the sets is smaller than that of the other. Report the mean and both standard deviations.

The following table shows the gas tax (in cents per gallon) in each of the southern U.S. states. (Source: 2017 World Almanac and Book of Facts) a. Find and interpret the median gas tax using a sentence in context. b. Find and interpret the interquartile range. c. What is the mean gas tax? d. Note that the mean for this data set is greater than the median. What does this indicate about the shape of the data? Make a graph of the data and discuss the shape of the data. $$ \begin{array}{|l|l|} \hline \text { State } & \begin{array}{c} \text { Gas Tax } \\ \text { (cents/gallon) } \end{array} \\ \hline \text { Alabama } & 39.3 \\ \hline \text { Arkansas } & 40.2 \\ \hline \text { Delaware } & 41.4 \\ \hline \text { District of } & \\ \text { Columbia } & 41.9 \\ \hline \text { Florida } & 55 \\ \hline \text { Georgia } & 49.4 \\ \hline \text { Kentucky } & 44.4 \\ \hline \text { Louisiana } & 38.4 \\ \hline \end{array} $$ $$ \begin{array}{|l|l|} \hline \text { State } & \begin{array}{c} \text { Gas Tax } \\ \text { (cents/gallon) } \end{array} \\ \hline \text { Maryland } & 51 \\ \hline \text { Mississippi } & 37.2 \\ \hline \text { N. Carolina } & 53.7 \\ \hline \text { S. Carolina } & 35.2 \\ \hline \text { Tennessee } & 39.8 \\ \hline \text { Texas } & 38.4 \\ \hline \text { Virginia } & 40.7 \\ \hline \text { W. Virginia } & 51.6 \\ \hline \end{array} $$
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