Normal Distribution and Percentiles

If I tell you that you scored at the 55th percentile on your final exam, you would know:

• 55% of the class scored the same or worse than you did

• You earned a 55% on the exam

• You failed the exam

• 45% of the class scored worse than you did

Given the data set: 1, 2, 3, 6, 9, 11, 45, 102, calculate the percentile rank for 11.

• 70

• 62.5

• 72.5

• 75

Jeremy scored a 74 on his test. 16 of the 26 scores on the test are less than or equal to 74. What is Jeremy's percentile rank?

• 62nd percentile

• 38th percentile

• 74th percentile

• 26th percentile

Shannon spent $60 on her homecoming dress. If 197 of the 300 students that bought a homecoming dress spent more than Shannon, what is the percentile rank of her cost?

• 103rd percentile

• 34th percentile

• 66th percentile

• 20th percentile

A 12 oz. can of soda has a mean volume of 12 oz, with a standard deviation of 0.25 oz. What is the percentile for a soda that only has 11.5 oz.?

• 3rd percentile

• 16th percentile

• 50th percentile

• 84th percentile

At a local high school, GPAs are normally distributed with a mean of 2.9 and a standard deviation of 0.6. If you have a GPA of 4.1, what is your percentile?

• 50th percentile

• 84th percentile

• 98th percentile

• 2.5 percentile

At a high school, GPAs are normally distributed with a mean of 2.9 and a standard deviation of 0.6. Find the z-score of a GPA of 3.2? What percentile is this?

• z=0.5, 67th percentile

• z=0.5, 69th percentile

The mean life of a tire is 30,000 km. The standard deviation is 2000 km. What is the z-score of a tire that lasts 27, 500 miles. What percentile is this?

• z=-1.25, 9th percentile

• z=-1.25, 11th percentile

The shelf life of a particular dairy product is normally distributed with a mean is 12 days and a standard deviation of 3 days. Find the z-score of a dairy product that has a shelf life of 14 days. What percentile is this?

• z=0.33, 50th percentile

• z=0.66, 75th percentile

• z=0.66., 84th percentile

Pat and Chris both took a spatial abilities test (mean=80, standard deviation=8). Pat scored a 76 and Chris scored a 94. Find z-scores for Pat and Chris. What are their percentiles?

• Pat's z-score=0.5 with a 31st percentile. Chris's z-score=1.75 with a 96th percentile.

• I didn't do this problem, so I am going to guess B.