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The scores on a mathematics college-entry exam are normally distributed with a mean of 68 and standard deviation 7.2. Students scoring higher than one standard deviation above the mean will not be enrolled in the mathematics tutoring program. how many of the 750 incoming students can be expected to be enrolled in the tutoring program?

a. 631
b. 512
c. 238
d. 119

User XGouchet
by
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1 Answer

1 vote

Answer:

d. 119

Explanation:

To solve this problem, we first need to find the cutoff score for the mathematics tutoring program.

One standard deviation above the mean is equal to:

68 + 1(7.2) = 75.2

Therefore, students scoring higher than 75.2 will not be enrolled in the mathematics tutoring program.

Next, we need to find the proportion of students who score lower than 75.2. To do this, we can use the standard normal distribution table or a calculator to find the z-score corresponding to a score of 75.2:

z = (x - μ) / σ = (75.2 - 68) / 7.2 = 1.022

Using the standard normal distribution table or a calculator, we can find that the proportion of students scoring lower than a z-score of 1.022 is approximately 0.8461.

Therefore, the proportion of students scoring higher than 75.2 is:

1 - 0.8461 = 0.1539

To find the number of students out of 750 who can be expected to be enrolled in the mathematics tutoring program, we can multiply the proportion by the total number of students:

0.1539 x 750 ≈ 115

Therefore, the answer is approximately 115 students, which is closest to option (d) 119.

User BinaryBucks
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