1.Givenzis the standard normal random variable, findc>0

such that

P(-c

c=

2.The annual rainfall in a certain region is approximately normally distributed with mean 41.4 inches and standard deviation 5.8 inches. Round answers to the nearest tenth of a percent.

a) What percentage of years will have an annual rainfall of less than 43 inches?%

b) What percentage of years will have an annual rainfall of more than 39 inches?%

c) What percentage of years will have an annual rainfall of between 38 inches and 42 inches?

3.A particular fruit's weights are normally distributed, with a mean of 601 grams and a standard deviation of 9 grams.

If you pick one fruit at random, what is the probability that it will weigh between 591 grams and 593 grams:

4.A particular fruit's weights are normally distributed, with a mean of 523 grams and a standard deviation of 19 grams.

The heaviest 13% of fruits weigh more than how many grams?

Give your answer to the nearest gram.

5.Colton and Jesse began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. Colton took a test in Math and earned a 75.1, and Jesse took a test in Art History and earned a 68. Use the fact that all the students' test grades in the Math class had a mean of 72.6 and a standard deviation of 10.2, and all the students' test grades in Art History had a mean of 64.4 and a standard deviation of 11.1 to answer the following questions.

a)Calculate the z-score for Colton's test grade.

Z=

b)Calculate the z-score for Jesse's test grade.

z=

c)Which person did relatively better?

• Colton
• Jesse
• They did equally well.

6.A population of values has an unknown distribution with

=21.6and=37.6

. You intend to draw a random sample of sizen=19

a)What is the mean of the distribution of sample means x=

(Please enter an exact answer.)

b)What is the standard deviation of the distribution of sample means x=

7.A population of values has a normal distribution with =219.6 and=8.5

You intend to draw a random sample of sizen=14

First calculatez, round it to two (2) decimal places, then use the roundedz

-score to determine the required probability accurate to four (4) decimal places.

(Please report your answer accurate to 2 decimal places.)

a)Find the probability that a single randomly selected value is less than 223.9.

P(x<223.9)=

b)Find the probability that a sample of sizen=14

is randomly selected with a mean less than 223.9.

P(x<223.9)=

8.The number of trades (in thousands) completed daily by an online stock brokerage follows a normal distribution with a mean of 107.4 and a standard deviation of 24.6. On average, the brokerage receives $8.4 commission per trade.

For samples of sizen=18days:

1. Determine the mean and standard deviation of the sampling distribution of the sample mean daily commissions received (in thousand dollars) accurate to 3 decimal places:

a) Mean = (thousand dollars)

b)Standard deviation = (thousand dollars)

2.Determine the following probabilities (as percentages) accurate to one (1) decimal place.

What is the probability that the mean daily commissions received is

a) more than $841,680? (%)

b)between $832,440 and $994,560? (%)

3.For the given sample size, what is the minimum average daily commissions receivable from the highest 20% volume trading days?

Round to the nearest thousand dollars.