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1. The ages of members of an online gaming group are normally distributed with a mean of 23 years and a standard deviation of 4 years.

There are 300 members in the group.

About how many members are expected to be between 15 years old and 31 years old?

 

a. 204

b. 264

c. 270

d. 285

 

2. 

Use technology or a z-score table to answer the question.

The expression  P(z<1.27) represents the area under the standard normal curve below the given value of z.

What is  P(z<1.27)?

 

a. 0.1020

b. 0.1038

c. 0.8962

d. 0.8980

3.  

Use technology or a z-distribution table to find the indicated area.

The weights of grapefruits in a bin are normally distributed with a mean of 261 grams and a standard deviation of 9.4 grams.

Approximately 20% of the grapefruits weigh less than which amount?

 

a. 239 g

b. 247 g

c. 253 g

d. 261 g

4. 

Suppose the scores on a grammar quiz are normally distributed with a mean of 76 and a standard deviation of 8.

Which group describes 16% of the population of grammar quiz scores?

 

a. scores below 60

b. scores below 68

c. scores above 80

d. scores above 94

5. 

Select Yes or No to state whether each data set is likely to be normally distributed.

 

the age of people entering a super store (yes or no)

the heights of people entering a super store (yes or no)

the number of 8 oz glasses of milk in 1 gallon (yes or no)

the gallons of milk sold at the super store in one week (yes or no)

6. 

The masses of the oranges on sale at a farm stand are normally distributed with a mean of 239 grams and a standard deviation of 25 grams.

 

Enter the z-score of an orange that has a mass of 259 grams.

7. 

The heights of the peach trees in an orchard are normally distributed with a mean of 12.5 feet and a standard deviation of 1.8 feet.

What is the height of a peach tree with a z-score of −0.5 ?

Enter your answer, rounded to the nearest tenth

8. 

Use technology or a z-distribution table to find the indicated area.

The masses of the eggs collected on a farm are normally distributed with a mean of 55 grams and a standard deviation of 4.2 grams.

Approximately 80% of the eggs on the farm have a mass greater than which mass?

 

a. 51.5 g

b. 54.1 g

c. 55.8 g

d. 58.5 g

9. 

Use technology or a z-score table to answer the question.

The scores on a memory test are normally distributed with a mean of 100 and a standard deviation of 25. Consider a group of 400 people who take the test.

How many people will score 90 or less?

 

a. 63

b. 138

c. 180

d. 262

 Apr 17, 2019
 #1
avatar+5232 
+1

1)

 

You could do this problem the rigorous way and look up the probability of the high and low z-scores,

but because each of the bounds are integer multiples of the standard deviation, -2, and 2, about the mean,

I suspect they want you to know that

\(P[(\mu -\sigma,\mu+\sigma)]\approx 0.68\\ P[(\mu -2\sigma,\mu+2\sigma)] \approx 0.95\\ P[(\mu-3\sigma, \mu+3\sigma)] \approx 0.997\\ \text{etc.}\)

 

So we are looking at 95% of the total population of 300 gamers.

 

This is 285 people.

 Apr 17, 2019

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