The average starting salary of individuals with a master's degree in statistics is normally distributed with a mean of $48,000 and a standard deviation of $6,000. What is the probability that a randomly selected individual with a master's in statistics will get a starting salary of at least $55,000?
A)0.121
B)0.891
C)0.379
D)0.098

Question

Quizplus · Accepted Answer

To find the probability that a randomly selected individual with a master's in statistics will get a starting salary of at least $55,000, we use the Z-score formula: Z = (X - μ) / σ, where X is the value of interest ($55,000), μ is the mean ($48,000), and σ is the standard deviation ($6,000). Plugging in the values, we get Z = ($55,000 - $48,000) / $6,000 = 7,000 / 6,000 = 1.167. Looking up the Z-score of 1.167 in a standard normal distribution table or using a calculator, we find that the area to the left of this Z-score is approximately 0.879. Since we want the area to the right (the probability of earning at least $55,000), we subtract this value from 1, giving us 1 - 0.879 = 0.121.

The Average Starting Salary of Individuals with a Master's Degree