# Probability & Statistics: Exam Review Day 1

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"Probability & Statistics: Exam Review Day 1"

```					                            Probability & Statistics: Exam Review

Confidence Intervals for Means (Large and Small Sample Sizes)

Confidence Intervals for the mean:           xE    xE
                                          s 
Large sample size: E  Zc                 Small sample size: E  tc    
 n                                         n

Minimum Sample Size
 Z c  
2

Minimum sample size for the mean: n          
 E 

Directions: Construct a confidence interval at the given level for the population mean based on
the sample mean.
1. A manager of a baseball stadium wished to construct a 90% confidence interval for the average
age of all baseball fans. In a random sample of 40 fans, the mean age was 32.5 years with a standard
deviation of 2.3 years. Construct the interval. Why would the manager find this information useful?

2.     A random sample of 15 computers has an average price of \$870 with a standard deviation of
\$51. The principal of a high school wants to construct a 98% confidence interval for the average
price. Construct the interval for her.

3.     A random sample of 22 dogs found the average weight to be 11.2 lbs with a standard deviation
of 2.1 lbs. Construct an 80% confidence interval for the average weight of the dogs.

4. The school nurse surveys 30 girls and finds the average weight of these girls to be 134 pounds
with a standard deviation of 12 pounds. Construct a 99% confidence interval for the nurse and tell
how she might use this information.

Directions: Determine the minimum sample size.
5. A company is manufacturing bolts for a picnic table. The bolt must meet the specifications of
being within 2 millimeters of the standard deviation of 6 millimeters. Determine the minimum
required sample size to be tested if you want to be 95% confident.

6. A hotel CEO wishes to estimate the average length of employment for his managers. The CEO
wants to have an error of tolerance of 2 year. Determine the minimum sample size required to
construct a 99% confidence interval. Use a standard deviation of 3.5 years.
Probability & Statistics: Exam Review

Confidence Intervals for Means (Large and Small Sample Sizes)

Confidence Intervals for the mean:           xE    xE
                                          s 
Large sample size: E  Zc                 Small sample size: E  tc    
 n                                         n

Minimum Sample Size
 Z c  
2

Minimum sample size for the mean: n          
 E 

Directions: Construct a confidence interval at the given level for the population mean based on
the sample mean.
1. A manager of a baseball stadium wished to construct a 90% confidence interval for the average
age of all baseball fans. In a random sample of 40 fans, the mean age was 32.5 years with a standard
deviation of 2.3 years. Construct the interval. Why would the manager find this information useful?

2.     A random sample of 15 computers has an average price of \$870 with a standard deviation of
\$51. The principal of a high school wants to construct a 98% confidence interval for the average
price. Construct the interval for her.

3.     A random sample of 22 dogs found the average weight to be 11.2 lbs with a standard deviation
of 2.1 lbs. Construct an 80% confidence interval for the average weight of the dogs.

4. The school nurse surveys 30 girls and finds the average weight of these girls to be 134 pounds
with a standard deviation of 12 pounds. Construct a 99% confidence interval for the nurse and tell
how she might use this information.

Directions: Determine the minimum sample size.
5. A company is manufacturing bolts for a picnic table. The bolt must meet the specifications of
being within 2 millimeters of the standard deviation of 6 millimeters. Determine the minimum
required sample size to be tested if you want to be 95% confident.

6. A hotel CEO wishes to estimate the average length of employment for his managers. The CEO
wants to have an error of tolerance of 2 year. Determine the minimum sample size required to
construct a 99% confidence interval. Use a standard deviation of 3.5 years.

```
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