Answer:
Therefore, 95% of beginning salaries will fall between $42,032.40 and $60,447.60.
Explanation:
a) To find the percentage of beginning salaries between $37,850 and $65,630, we need to standardize the values using the z-score formula:
z1 = (37850 - 51740) / 4630 = -3.00
z2 = (65630 - 51740) / 4630 = 3.00
Using a standard normal distribution table or calculator, we can find the area under the curve between -3.00 and 3.00 to be approximately 99.7%. Therefore, approximately 99.7% of beginning salaries will be between $37,850 and $65,630.
b) To find the two values between which 95% of beginning salaries will fall, we need to find the z-scores that correspond to the 2.5th and 97.5th percentiles of the standard normal distribution. These z-scores are approximately -1.96 and 1.96, respectively.
We can use these z-scores to find the corresponding salary values:
z1 = (x1 - 51740) / 4630 = -1.96
x1 = -1.96 * 4630 + 51740 = $42,032.40
z2 = (x2 - 51740) / 4630 = 1.96
x2 = 1.96 * 4630 + 51740 = $60,447.60
Therefore, 95% of beginning salaries will fall between $42,032.40 and $60,447.60.