Question

A survey found that the mean amount customers spend for a valentine's gift for their pets is $5.05. Assume the distribution of the amount spent is approximately normal and the standard deviation is $0.56. If a random sample of 47 pet owners is selected, find the probability that the mean amount spent of the sample will be less than $5.30. Round intermediate value calculations to two decimal places, and the final answer to four decimal places.

Answer 1

To find the probability that the mean amount spent of the sample will be less than $5.30 for a valentine's gift for their pets, you need to calculate the z-score and use the standard normal distribution table. The probability is approximately 0.9941.

Step-by-step explanation:

To find the probability that the mean amount spent of the sample will be less than $5.30, we need to calculate the z-score and then use the standard normal distribution table.

First, let's calculate the z-score using the formula: z = (x - μ) / (σ / sqrt(n)), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Plugging in the values, we get: z = ($5.30 - $5.05) / ($0.56 / sqrt(47)) ≈ 2.53

Next, we can use the standard normal distribution table or a calculator to find the probability associated with the z-score. From the table, we find that the probability is approximately 0.9941.