Question

Please help me with this multiple question!! :

Scores on a standardized exam are normally distributed with a mean of 59 and a standard deviation of 8. Consider a group of 5000 students.

Approximately how many students will score less than 67 on the exam?

A) 4039

B) 4195

C) 4207

D) 4219

Answer 1

C

Explanation:

Find P(X > 67)

using ( x - mean )/ standard deviation again you will get thi(1) which is equal to 0.8413....

0.8413 x 5000 is 4207

Answer 2

C) 4207

Explanation:

In the figure attached standard normal distribution can be seen. The area under the curve from
`\mu` = 0 to the left is 0.5. You have to find the area between
`\mu` = 0 and Z, where Z is computed as Z = (x - mean)/standard deviation and x is the point of your interest, in this case x = 67. This procedure is made in this way because the table show the case when mean = 0 and standard deviation = 1. So, Z = (67 - 59)/8 = 1 and area = 0.3413. In consequence, the probability of a student to get less than 67 is 0.3413 + 0.5 = 0.8413 (the area under the curve from the left to Z = 1). In terms of students, 0.8413*5000 = 4207