A final exam in math 160 has a mean of 73 with a standard deviation 7.73. Assume that a random sample of 24 students is selected and the test score of the sample is computed. Assuming the scores are normally distributed, what percentage of the samplerans are less than 70?

Answer 1

First, we need to calculate the standard error of the mean:

SE = σ/√n = 7.73/√24 ≈ 1.58

Next, we can standardize the sample mean using the formula:

z = (x̄ - μ)/SE

where x̄ is the sample mean, μ is the population mean (73), and SE is the standard error of the mean. Substituting the given values, we get:

z = (70 - 73)/1.58 ≈ -1.90

Using a standard normal distribution table or calculator, we can find that the percentage of samples with a mean less than 70 is approximately 2.28%. Therefore, we can conclude that about 2.28% of samples of size 24 would have a mean score less than 70 on the math 160 final exam, assuming the scores are normally distributed.