Question

Different dealers may sell the same car for different prices. The sale prices for a particular car are normally distributed with a mean and standard deviation of 26 thousand dollars and 2 thousand dollars, respectively. Suppose we select one of these cars at random. Let X= the sale price (in thousands of dollars) for the selected car. Find P(X>25), left parenthesis, X, is greater than, 25, right parenthesis. You may round your answer to two decimal places.

Answer 1

Answer:

P(X > 25) = 0.69

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using 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.

The sale prices for a particular car are normally distributed with a mean and standard deviation of 26 thousand dollars and 2 thousand dollars, respectively.

This means that $\mu = 26, \sigma = 2$

Find P(X>25)

This is 1 subtracted by the pvalue of Z when X = 25. So

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

$Z = \frac{25 - 26}{2}$

$Z = -0.5$

$Z = -0.5$ has a pvalue of 0.31

1 - 0.31 = 0.69.

So

P(X > 25) = 0.69