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 \[p(x>25)\]. you may round your answer to two decimal places.

Answer 1

To find the probability that a car's sale price is greater than $25,000, we can use the properties of the normal distribution. By converting the price to a z-score and using a standard normal distribution table, we can find that the probability is approximately 0.3085.

Step-by-step explanation:

This problem involves the normal distribution. Since the sale prices for a particular car are normally distributed, we can use the properties of the normal distribution to find the probability that the sale price is greater than $25,000.

To find P(x > 25), we need to calculate the area under the normal curve to the right of $25,000. We can do this by converting the sale price to a z-score using the formula z = (x - mean) / standard deviation, where x is the value we want to convert, mean is the mean of the distribution, and standard deviation is the standard deviation of the distribution.

Substituting the given values into the formula, we have z = (25 - 26) / 2 = -0.5. We then use a standard normal distribution table or a calculator to find the probability that z is greater than -0.5, which is approximately 0.6915. Therefore, P(x > 25) = 1 - 0.6915 = 0.3085.