The points obtained by students of a class in a test are normally distributed with a mean of 60 points and a standard deviation of 65 points. About what percent of students have scored between 60 and 65 points?

34%

Step-by-step explanation:

Since the points obtained by students of the class in a test are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = points obtained by students

µ = mean

σ = standard deviation

From the information given,

µ = 60 points

σ = 5 points

The probability of students that have scored between 60 and 65 points is expressed as

P(60 ≤ x ≤ 65)

For x = 60,

z = (60 - 60)/5 = 0

Looking at the normal distribution table, the probability corresponding to the z score is 0.5

For x = 65,

z = (65 - 60)/5 = 1

Looking at the normal distribution table, the probability corresponding to the z score is 0.84

Therefore,

P(60 ≤ x ≤ 65) = 0.84 - 0.5 = 0.34

Therefore, the percent of students that have scored between 60 and 65 points is

0.34 × 100 = 34%

8

step-by-step explanation:

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis: