at one college gpas are normally distributed with the mean of 3 and a standard deviation of 04 w

Step 1: Calculate the z-scores for GPA of 2.6 and 3.4 using the formula z = (X - μ) / σ, where X

At one college gpas are normally distributed with the mean...

At one college, GPAs are normally distributed with a mean of 3 and a standard deviation of 0.4. What percentage of students at the college have a GPA between 2.6 and 3.4? A) 84.13% B) 95.44% C) 68.44% D) 99.74%

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Transcript

00:01 In the question, let x represent the gpa of the students.

00:04 We have given mu means mean is equal to 3.

00:07 Standard deviation sigma is equal to 0 .4.

00:12 Standard normal variance z is equal to x minus mu divide by sigma.

00:19 It will be z.

00:21 We have given a student at the college have a gpa between 2 .6 between 2 .6, 2 .6 and 3 .6.

00:30 3 .4 and 3 .4 it means x1 is equal to 2 .6 and x2 is equal to 3 .4.

00:40 And the option is this option number a, option number b, option number c and option number d.

00:45 We have four options in this questions and we have given x1 and x2.

00:52 We know that probability of probability of x1 less than x x less than x less than x2 is equal to probability of x1 minus mu means we have given mu mu means mean is equal to 3 x1 minus mu minus mu divide by sigma less than z less than x2 minus mu divide by sigma now probability of x1 is equal to 2 .6 we have given 2 .6 minus mu is equal to 3 minus 3 divided by sigma.

01:36 Sigma is equal to we have given 0 .4.

01:39 This is 0 .4.

01:41 Less than x2.

01:44 X2 means 3 .4.

01:46 3 .4 minus sigma.

01:49 Sigma is 3.

01:50 Divide by mu is 3 and upon sigma divide by sigma, sigma is 0 .4...