The distribution of sample means for scores on a test for samples of size 100 is normal with a mean of 63.3 and a standard deviation of 1.5. If a sample of 100 test scores is selected at random, what is the probability that the sample mean will be less than 60.6?
A)0.9641
B)0.0668
C)1.8
D)0.0359

Question

Quizplus · Accepted Answer

To find the probability that the sample mean will be less than 60.6, we use the Z-score formula: Z = (X - μ) / σ, where X is the value of interest (60.6), μ is the mean of the distribution (63.3), and σ is the standard deviation of the distribution (1.5). Plugging in the values, we get Z = (60.6 - 63.3) / 1.5 = -2.7 / 1.5 = -1.8. Looking up -1.8 on the standard normal distribution table gives us a probability of approximately 0.0359.

The Distribution of Sample Means for Scores on a Test