The document contains examples of calculating z-scores from given means and standard deviations for normal distributions. It provides the z-scores that correspond to specific raw scores in several examples, and calculates areas under the normal curve for given ranges of z-scores or raw scores. It also calculates the percentage of students that would score below or between certain values based on the mean and standard deviation of their test scores.

2. MORE INFORMATIONS

3. Determine the z value for each of the following x values
for a normal distribution with 𝜇 = 16 𝑎𝑛𝑑 𝜎 = 3.
a. x = 12 b. x = 8 c. x = 22 d. x = 25

4. Given the mean 𝜇 = 50 𝑎𝑛𝑑 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝜎 = 4 of a
population of reading scores. Find the z-value that corresponds
to a score x = 58.
Thus, the z-value that
corresponds the raw
score 58 is 2 in a
population distribution.
The score is above
average.
Given: 𝜇 = 50, 𝜎 = 4 and x = 58

5. Locate the z-value that corresponds to PE score of 39
given that 𝜇 = 45 𝑎𝑛𝑑 𝜎 = 6 .
Thus, the z-value that
corresponds the raw
score 39 is -1 in a
population distribution.
The score of 39 is
below average.
Given: 𝜇 = 45, 𝜎 = 6 and x = 39

6. A consumer group tested a sample of 100 light bulbs. It found
that the mean life expectancy of bulbs was 842 h, with a
standard deviation of 90. One particular light bulb from the
DuraBright Company had a z-score of 1.2. What was the life
span on this light bulb?
The light bulb had a life
span of 950 h.
Given: z = 1.2, 𝜇 = 842, 𝜎 = 90
Find: x

7. For a continuous random variable that has a normal distribution
with mean of 20 and a standard deviation of 4, find the area
under the normal curve from x = 20 and 27.
Given: 𝜇 = 20, 𝜎 = 4 a. x = 20 b. x = 27

8. For a continuous random variable that has a normal distribution
with mean of 20 and a standard deviation of 4, find the area
under the normal curve from x = 20 and 27.
The area between z = 0
and z = 1.75 is 0.4599.
Therefore the area under
the normal curve between
x = 20 and x = 27 is
0.4599.

9. The scores of a group of students in a standardized test are normally
distributed with mean of 60 and standard deviation of 8. Answer the
following:
a. How many percent of the students got below 72?
Therefore, about 93.32% of the group got below 72.

10. The scores of a group of students in a standardized test are
normally distributed with mean of 60 and standard deviation of 8.
Answer the following:
b. What part of the group scored between 58 and 76?
Therefore, about 57.59% of the group
got a score between 58 and 76.

11. The scores of a group of students in a standardized test are
normally distributed with mean of 60 and standard deviation of 8.
Answer the following:
c. If there were 250 students who took the test, about how
many students scored higher than 64?
Since there were 250 students who took the
test, about (250)(0.3085) = 77.13 or 77
students got a score higher than 64.

14. Thank