Calculator Homework #

4

-

Probabilities

for

Normal

Random Variables

To find the probability for a

normal

variable:

1.

Press 2

nd

[DISTR] then 2 for normalcdf(

2.

Enter

lower bound, upper bound, mean, standard deviation

)

To find an x

-

value (

normal random

variable

) for a cumulative probability:

1.

Press 2

nd

[DISTR] then 3 for invnorm(

2.

Enter

cumulative probability, mean, standard deviation

)

Exercise 1

In a recent year, the ACT scores for high school students with an A or B grade point average were

normally dis

tributed 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.

a.

Find the probability that the student's ACT score is less than 20.

b.

Find the probability that the student's ACT

score is greater than 31.

c.

Find the probability that the student's ACT score is between 25 and 32.

d.

Find the probability that a student's ACT score is less than 21 or more than 33.

e.

Find the 80

th

percentile for ACT scores of high school students with an A or B GPA.

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.

a.

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

b.

The fastest 3% of her laps are under __________ seconds.

c.

The middle 80% of her la

ps are from __________ seconds to __________ seconds.