Question

In a set of 100 ACT scores that are normally distributed and with a mean of 23 and standard deviation of 4.69, a. How many scores are expected to be lower than 18.31 (one standard deviation below the mean)? B. How many of the 100 scores are expected to be below 32.38 (two standard deviations above the mean)?

Answer 1

A) 16 scores

B) 98 scores

Step-by-step explanation:

if we look at a normal distribution table, 50% + 34.13% of all scores will be greater than 18.31 (one standard deviation)

this means that 84.13% or 84 scores will be higher than 18.31, so 100 - 84 = 16 scores will be lower than 18.31

we follow a similar procedure for 2 standard deviations, where 50% + 47.72% of the scores will be lower than 32.38 (the other side of the bell curve)

this means that 97.72% or 98 scores will be lower than 32.38