P&S: Finding Values in a Normal Distribution

Find the z-score that corresponds to a cumulative area of 0.4761.

• -0.06
• 1.14
• -1.41
• 1.64

Find the z-score that has 12.71% of the distribution’s area to its right.

• -0.06
• 1.14
• -1.41
• 1.64

Find the z-score that corresponds to the percentile P_8.

• -0.06
• 1.14
• -1.41
• 1.64

Find the z-score that corresponds to the percentile P_95.

• -0.06
• 1.14
• -1.41
• 1.64

Find the z-score that corresponds to the percentile P_87.

• 1.13
• 1.14
• -1.41
• 1.64

Find the z-score for which 75% of the distribution’s area lies between –z and z. 

• -1.15 & 1.15 
• -0.15 & 0.15

The monthly phone bills in a city are normally distributed with a mean of 30$ and a standard deviation of 12$. Find the x-value that correspond to z-scores of –2.35.

• $1.80 
• $68.04
• $32.76

The monthly phone bills in a city are normally distributed with a mean of 30$ and a standard deviation of 12$. Find the x-value that correspond to z-scores of 3.17. 

• $1.80 
• $68.04
• $32.76

The monthly phone bills in a city are normally distributed with a mean of 30$ and a standard deviation of 12$. Find the x-values that correspond to z-scores of 0.23.

• $1.80 
• $68.04
• $32.76

Annual U.S. per capita orange use: μ =11.4 lb, σ = 3lb. What annual per capita use of oranges represents the 10th percentile?

• 7.56 lbs
• 13.42 lbs
• 8.29 lbs 
• 9.38 lbs