Question

Buisiness Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is 168000 dollars. Assume the standard deviation is 44000 dollars. Suppose you take a simple random sample of 61 graduates. Find the probability that a single randomly selected graduate has a salary between 175323.7 and 179267.2 dollars. P(175323.7 < X < 179267.2) = places.) (Enter your answers as numbers accurate to 4 decimal

Answer 1

To find the probability that a single randomly selected graduate has a salary between $175,323.7 and $179,267.2, we need to standardize the salaries using the z-score formula and then use the standard normal distribution table.

Step-by-step explanation:

To find the probability that a single randomly selected graduate has a salary between $175,323.7 and $179,267.2, we need to standardize the salaries using the z-score formula and then use the standard normal distribution table. The z-score formula is:

z = (x - mean) / standard deviation

Plugging in the values, we get:

z1 = (175,323.7 - 168,000) / 44,000

z1 = 0.1667

z2 = (179,267.2 - 168,000) / 44,000

z2 = 0.2564

Now, we can look up the corresponding probabilities in the standard normal distribution table:

P(0.1667 < Z < 0.2564) = P(Z < 0.2564) - P(Z < 0.1667)

P(0.1667 < Z < 0.2564) = 0.5987 - 0.5659

P(0.1667 < Z < 0.2564) = 0.0328

Therefore, the probability that a single randomly selected graduate has a salary between $175,323.7 and $179,267.2 is approximately 0.0328.