"A normal distribution of test scores has a mean of 38 and a standard deviation of 6. Everyone scoring at or above the 80th percentile gets placed in an advanced class. What is the cutoff score to get into the class

the cutoff score to get into the class is 43

Step-by-step explanation:

Since the scores on the test are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = scores on the test.

µ = mean score

σ = standard deviation

From the information given,

µ = 38

σ = 6

The probability value for the 80th percentile is 80/100 = 0.8

Looking at the normal distribution table, the z score corresponding to the probability value is 0.85

Therefore,

0.85 = (x - 38)/6

Cross multiplying by 6, it becomes

0.85 × 6 = x - 38

5.1 = x - 38

x = 5.1 + 38

x = 43.1

Approximately 43

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.

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