Asked by Angela Scamardella on May 13, 2024
Verified
The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000.What is the probability that a randomly selected individual with an MBA degree will get a starting salary of at least $47,500?
A) 0.4332
B) 0.9332
C) 0.0668
D) 0.5000
Normally Distributed
Describes a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.
Starting Salaries
The initial amount of money that an employee earns annually when beginning a new job.
Standard Deviation
A system for evaluating the degree of dispersion or deviation among a collection of statistics.
- Decode the implications of the mean and standard deviation for distributions that are relevant to practical experiences.
Verified Answer
SD
Sofia Dela GarzaMay 16, 2024
Final Answer :
C
Explanation :
To find the probability that a randomly selected individual with an MBA degree will get a starting salary of at least $47,500, we use the Z-score formula: Z = (X - μ) / σ, where X is the value of interest ($47,500), μ is the mean ($40,000), and σ is the standard deviation ($5,000). Plugging in the values, we get Z = ($47,500 - $40,000) / $5,000 = 1.5. Looking up the Z-score of 1.5 in a standard normal distribution table or using a calculator, we find that the area to the left of Z = 1.5 is approximately 0.9332. Since we're interested in the probability of earning at least $47,500, we look for the area to the right, which is 1 - 0.9332 = 0.0668.
Learning Objectives
- Decode the implications of the mean and standard deviation for distributions that are relevant to practical experiences.