Calculator Homework #5 - Probabilities for Normally Distributed Random Variables

To find the probability for a normal variable:

1. Press 2^nd [DISTR] then 2 fornormalcdf(
2. Enter lower bound, upper bound, mean, standarddeviation)

To find an x-value (quantile score) for a cumulative probability:

1. Press 2^nd [DISTR] then 3 forinvnorm(
2. Enter cumulative probability, mean, standarddeviation)

Exercise 1

In a recent year, the ACT scores for high school students with an A or B grade point average were normally distributed with a mean of 24.2 and a standard deviation of 4.2. A student with an A or B average who took the ACT during this time is selected.

1. Find the probability that the student's ACT score is less than20.

1. Find the probability that the student's ACT score is greater than31.

1. Find the probability that the student's ACT score is between 25 and32.

1. Find the probability that a student's ACT score is less than 21 or more than33.

1. Find the 80^th percentile for ACT scores of high school students with an A or BGPA.

Exercise 2

Terri Vogel, an amateur motorcycle racer, averages 129.71 seconds per 2.5 mile lap (in a seven-lap race) with a standard deviation of 2.28 seconds. The distribution of her race times is normally distributed.

We are interested in one of her randomly selected laps.

1. Find the percent of her laps that are completed in less than 130seconds.

1. The fastest 3% of her lapsareunder seconds.

1. The middle 80% of her lapsare from secondsto seconds.