The starting salaries of individuals with an mba degree are...

The starting salaries of individuals with an MBA degree are normally distributed with a mean of $60,000 and a standard deviation of $7,500. a. What proportion of starting salaries are more than $50,000? b. Twenty-five percent of starting salaries are below what salary? c. Take a SRS of 25 recent MBA graduates. The calculated sample mean is $63,000. What is the probability of getting a sample mean starting salary greater than $63,000.

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00:01 Hello students, in this question, we are going to consider, let x be a random variable that starting salaries of the individual within an mba degree.

00:19 So, mu is nothing but mean, that is 60 ,000.

00:24 Then standard deviation is equals to 7500.

00:30 So that, i can able to write z is equals to x minus mu divided by sigma.

00:36 So, x minus 60 ,000, the whole divided by 7500 follows the standard normal.

00:46 So, in question number 8 is given, probability of x is greater than 50 ,000, that is probability of x minus mu divided by sigma is greater than 50 ,000 minus 60 ,000, the whole divided by 7500.

01:10 So, by simplifying it, we'd be getting probability of z, that is probability of z, which is greater than minus 1 .333.

01:22 So, that is 1 minus probability of z is less than minus 1 .33.

01:30 So, we need to simplify, that is 1 minus 0 .091217.

01:39 So, that is 0 .908783.

01:44 Now, let's move on to question number b.

01:47 Here, we need to find the x naught.

01:50 So, we need to find x naught, that is probability of x less than x naught is equals to 0 .25, that is probability of x minus mu divided by sigma less than x naught minus 60 ,000, the whole divided by 7500.

02:12 So, this is equals to 0 .25, that is probability of z is less than x naught minus 60 ,000, the whole divided by 7500...

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