Normal Distribution and Z Scores

The value of the mean and standard deviation of a standard normal distribution is __ and __ respectively.

• 0 and 1

• 1 and 0

The wider the width of the normal curve, the

• higher its peak

• larger its sd

• lower its peak

• smaller its sd

What is the area for the left side of the curve from the mean?

• 1

• 0.75

• 0.5

• 0.25

How many standard scores is 14 located if a set of scores is normally distributed with a mean of 12 and a standard deviation of 0.5?

• 2 standard scores to the left

• 2 standard scores to the right

• 4 standard scores to the left

• 4 standard scores to theright

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

• True

• False

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

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

The scores on a university examination are Normally distributed with a mean of 62 and a standard deviation of 11. If the bottom 5% of students will fail the course, what is the lowest mark that a student can have and still be awarded a passing grade?

• 40

• 43

• 44

• 57

• 62

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

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.