Finding Z-Scores, Standard Deviation, Mean and X

Composite scores on the ACT are normally distributed with a mean of 21 and standard deviation of 5. Find the z-score for a student that gets a 31.

• -2.00

• 2.00

• 1.50

• 0.00

Composite scores on the ACT are normally distributed with a mean of 21 and standard deviation of 5. Find the z-score for a student that scores a 28.

(a)  

Home prices in a certain neighborhood are normally distributed with a mean of $200,000 and a standard deviation of $10,000. Which of the following is the z-score for a home that costs $193,000?

• -$0.70

• $0.70

• -0.70

• 0.70

What is the correct formula for finding z-scores?

There are 100 franchises of Betty's Boutique in similar shopping malls across America. The gross Saturday sales of these boutiques are approximately normally distributed with a mean of $4610 and a standard deviation of $370.

Find the z-score of a gross Saturday sales amount of $4425.

Mathematical Equivalence

ON

In a given dataset 52% of data falls above 119. The dataset has a standard deviation of 5.2. If you were going to use the z-score formula to calculate a missing value, what would you substitute in for each of the following values?

• Unknown

• 5.2

• 119

• 0.52

For a test with a mean score of 81 and a standard deviation of 5, your score is 78. How would you use the z-score formula to find the standardized score, z?

a

b

c

d

81

5

78

-0.6

There are 100 franchises of Betty's Boutique in similar shopping malls across America. The gross Saturday sales of these boutiques are approximately normally distributed with a mean of $4610 and a standard deviation of $370. Find the z-score of a gross Saturday sales amount of $3870.

Mathematical Equivalence

ON

Suppose a data set is represented by a normal distribution with a mean of 10 and a standard deviation of 2.

What is z-score for a data of 17?

Mathematical Equivalence

ON

The mean weight of newborn infants is 7 pounds and the standard deviation is 0.8 pounds. The weights of newborn infants are normally distributed. Find the z-score for a weight of 9 pounds.

Mathematical Equivalence

ON