Question

For a sample of n=62​, the probability of a sample mean being less than 21.3 if μ=21 and σ=1.35 is

Answer 1

The probability that the sample mean is between 85 and 92 is 0.3564, or 35.64%.

Step-by-step explanation:

To find the probability that the sample mean is between 85 and 92, we need to calculate the z-scores for both values using the formula:

z = (x - μ) / (σ / √n)

With μ = 90, σ = 15, and n = 25, we can calculate:

z1 = (85 - 90) / (15 / √25) = -1

z2 = (92 - 90) / (15 / √25) = 0.5385

Next, we need to find the area under the standard normal curve between these z-scores. Using a standard normal distribution table or a calculator, we find:

Area between z = -1 and z = 0.5385 = 0.3564

Therefore, the probability that the sample mean is between 85 and 92 is 0.3564, or 35.64%.