Question

The scores of a recent test taken by 1200 students had an approximately normal distribution with a mean of 225 and a standard deviation of 18. determine the number of students who scored between 200 and 245

Answer 1

If the probability will be 0.7842. Then the number of students who scored between 200 and 245 will be 941.

What is a normal distribution?

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

The scores of a recent test taken by 1200 students had an approximately normal distribution with a mean of 225 and a standard deviation of 18.

Then the number of students who scored between 200 and 245 will be

Then the z-score for x = 200

$z = \dfrac{200-225}{18}\\\\z = -1.389$

Then the z-score for x = 245

$z = \dfrac{245-225}{18}\\\\z = 1.1111$

Then we have

$\begin{aligned} P(-1.39 < z < 1.11) &= P(z < 1.11) - P(z < -1.389)\\\\&= P(z < 1.11)- [1-P(z > -1.389)] \\\\&=0.8665 - (1-0.9177) \\\\&=0.7842 \end$

Then the number of students who scored between 200 and 245 will be

→ 0.7842 × 1200

→ 941.04 ≅ 941

More about the normal distribution link is given below.

https://brainly.com/question/12421652

#SPJ1