Question

The price of entrées at fast food restaurants in the area have an unknown distribution with a mean price of $7.15 and a standard deviation of $1.25. If you randomly select 43 combo meals around town, what is the probability that their average price will be less than $7.00?

Answer 1

If you randomly select 43 combo meals around town, the probability that their average price will be less than $7.00 is 0.2148.

In Mathematics, the Central Limit Theorem states that the sampling distribution of means would always be normally distributed, as long as the sample size is large enough.

In order to determine the standard deviation of the sampling distribution, we divide the population standard deviation by the square root of the sample size:

σx = σ/√n

σx = 1.25/(√43)

σx ≈ 0.1906

Next, we would determine the z-score as follows;

Z-score, z = (X - μ)/σx

Z-score, z = (7.00 - 7.15)/0.1906

Z-score, z = -0.79

Based on the standardized normal distribution table, the required probability is given by:

P(X < 7.00) = 1 - P(x > Z)

P(X < 7.00) = 1 - P(x > -0.79)

P(X < 7.00) = 1 - 0.7852

P(X < 7.00) = 0.2148