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A bookstore sells books for $2, $3, and $5. Let random variable X = "amount of money for one book."Look at the relative-frequency table below representing the amount of money spent on one item and the relative frequencies with which customers purchase them.x P(X = x)2 .723 .155 .13If the expected amount of money spent by a customer is $2.54, what is the standard deviation?

Question

A bookstore sells books for 2,2, 3, and 5.LetrandomvariableX="amountofmoneyforonebook."Lookattherelative−frequencytablebelowrepresentingtheamountofmoneyspentononeitemandtherelativefrequencieswithwhichcustomerspurchasethem.xP(X=x)2.723.155.13Iftheexpectedamountofmoneyspentbyacustomeris5. Let random variable X = "amount of money for one book."Look at the relative-frequency table below representing the amount of money spent on one item and the relative frequencies with which customers purchase them.x P(X = x)2 .723 .155 .13If the expected amount of money spent by a customer is 2.54, what is the standard deviation?

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Solution

To calculate the standard deviation, we first need to calculate the variance. The variance is the average of the squared differences from the mean (expected value).

Here are the steps:

  1. Calculate the squared difference from the mean for each value of X.

    (2-2.54)^2 * 0.72 = 0.1872 (3-2.54)^2 * 0.15 = 0.033 (5-2.54)^2 * 0.13 = 0.3182

  2. Add these values together to get the variance.

    0.1872 + 0.033 + 0.3182 = 0.5384

  3. The standard deviation is the square root of the variance.

    sqrt(0.5384) = 0.7338

So, the standard deviation of the amount of money spent by a customer is approximately $0.73.

This problem has been solved

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