Normal Distribution with Z Score

Find the z-score for 75 given a mean of 60 and a standard deviation of 6.

• -2.5

• 2.5

• -1.15

• 1.15

Find the z-score for 48 given a mean of 50 and a standard deviation of 5.

• 2.5

• -2.5

• -0.4

• 0.4

Find the z-score for 62 given a mean of 30 and a standard deviation of 20.

• 1.6

• -1.6

• 11.6

• -11.6

Find the area under the standard normal curve that lies to the left of z=2.1.

• 79%

• -1.79%

• 98.21%

• 0.98%

The weight of adult male grizzly bears living in the wild in the continental United States is approximately normally distributed with a mean of 500 pounds and a standard deviation of 50 pounds. The weight of adult female grizzly bears is approximately normally distributed with a mean of 300 pounds and a standard deviation of 40 pounds. Approximately, what would be the weight of a female grizzly bear with the same standardized score (z-score) as a male grizzly bear with a weight of 530 pounds?

• 276 pounds

• 324 pounds

• 330 pounds

• 340 pounds

• 530 pounds

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The heights of students in a class follow a normal distribution with a mean of 65 inches and a standard deviation of 3 inches. John is 70 inches tall, while Sarah is 67 inches tall. Calculate the z-scores for John and Sarah and determine who is taller than their peers.

• John is relatively taller than Sarah.

• Sarah is relatively taller than John.

• John and Sarah are equally tall.

• insufficient information to determine who is relatively taller.

The average waist size for teenage males is 29 inches with a standard deviation of 2 inches. 
If waist sizes are normally distributed, determine the z-score of a teenage male with a 33 inch waist.  

• 2

• 1

• -2

• -1

In a normal distribution, the z-score for the mean is 0.

• True

• False

The average waist size for teenage males is 29 inches with a standard deviation of 1.4 inch. If waist sizes are normally distributed, estimate the proportion of teenagers who will have waist sizes greater than 31 inches?

• 92.4%

• 10.5%

• 16%

• 7.6%

Steve took his math test and scored an 88. If the class average was a 78 with a standard deviation of 5, what percent of students earned a grade that was higher than Steve's grade?

• .9772

• .93

• .05

• .0228