Question

learning goal
i can determine when a data set warrants a normal distribution. i
can determine the mean and standard deviation of a data set and
fit it to a normal distribution. i can estimate population
percentages based on mean, standard deviation, and distribution.
i can estimate the areas under the normal curve using calculators,
spreadsheets, and tables.
lesson 23.2 checkpoint
once you have completed the above problems and checked your solutions, complete the lesson checkpoint
below.
complete the lesson reflection above by circling your current understanding of the learning goal.
use the standard normal table below to answer question 2.
standard normal table ( z _ { x } = \frac { x - mu } { sigma } )

1. a college - entrance exam is designed so that scores are normally distributed with a mean of 500 and a

standard deviation of 100. what percent of exam scores are between 400 and 600?

1. suppose the scores on a test given to all juniors in a school district are normally distributed with a mean of

74 and a standard deviation of 8. using the standard normal table above, find the percent of juniors whose
score is less than 86.

Explanation:

Step1: Calculate the z - score for \(x = 86\)

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(\mu = 74\) (mean) and \(\sigma=8\) (standard deviation).

$$z=\frac{86 - 74}{8}=\frac{12}{8}=1.5$$

Step2: Find the value in the standard - normal table

Looking at the standard - normal table, for \(z = 1.5\), we look at the row labeled \(1\) and the column labeled \(0.5\). The value in the table is \(0.9332\)

Answer:

\(93.32\%\)