Question

Let x be a continuous random variable that follows a distribution skewed to the left with u = 88 and = 18. Assuming n/N< 0.05,

find the probability that the sample mean, X, for a random sample of 60 taken from this population will be
a. less than 82.5.
b. greater than 87.6.

Answer 1

To find the probability of the sample mean being less than or greater than a certain value, we need to standardize the sample mean using the z-score formula and calculate the corresponding probabilities.

Step-by-step explanation:

To find the probability that the sample mean, X, for a random sample of 60 will be less than 82.5, we need to standardize the sample mean using the z-score formula. The z-score formula is z = (X - u) / (sigma / sqrt(n)), where X is the sample mean, u is the population mean, sigma is the population standard deviation, and n is the sample size.

For part a, we calculate the z-score as z = (82.5 - 88) / (18 / sqrt(60)). Then we can look up the z-score in the standard normal distribution table or use a calculator to find the corresponding probability.

For part b, we follow the same steps as part a but use the sample mean of 87.6 instead. Find the z-score and the corresponding probability.