# Algebra 2 Why Does Delta Overbook: Normal Distributions Name______Class Period______

Algebra 2 Why Does Delta Overbook: Normal Distributions

Do Section 12.7: p. 749 # 19-22

19. ______20. ______

21. ______22. ______

1) A company produces light bulbs having a life expectancy that is normally distributed with a mean of 1000 hours and a standard deviation of 50 hours.

a) Label the mean and the correct value for each standard deviation mark on the curve.

b) What percent of the bulbs will last for 1000 hours or more?

c) What is the probability that a randomly chosen bulb will burn out in 900 hours or less?

d) What is the probability that a randomly chosen bulb will last between 850 and 1050 hours?

2) A survey showed that an average of 332 students at Logan High see a movie in a theater each month. The standard deviation is 16.

a) Label the mean and the correct value for each standard deviation mark on the curve.

b) On any given month, what is the probability that more than 348 students see a movie in a theater?

c) What is the probability on any given month that between 300 and 348 students see a movie in a theater?

3) The test scores for an Algebra 2 math test are normally distributed with a mean of 75 and a standard deviation of 7.5.

a) Label the mean and the correct value for each standard deviation mark on the curve.

b) What is the range of the middle 68% of the students?

c) The top 2.5% in the class scored above what value?

d) Where is the 50th Percentile?

e) The 25th percentile is at 70 points and the 75thpercentile is at 80 points. Mark the approximate location of these scores on the curve. Create a box and whisker plot under the normal curve.

f) The 90th percentile is at 85 points. If there are 36 students in class, how many students scored below 85 points? ______How many scored above 85 points? ______

Extra Credit: Use what you know about the 90th percentile to find the score for the 10th percentile.

Name______Class Period______

Algebra 2 Why Does Delta Overbook: Normal Distributions

Do Section 12.7: p. 749 # 19-22

19. 50%20. 15.8% or 15.85%

21. 2.4% or 2.5%22. 27.2% or 27%

1) A company produces light bulbs having a life expectancy that is normally distributed with a mean of 1000 hours and a standard deviation

of 50 hours.

a) Label the mean and the correct value for each standard deviation mark on the curve.

b) What percent of the bulbs will last for 1000 hours or more?50%

c) What is the probability that a randomly chosen bulb will burn out in 900 hours or less?2.4%

d) What is the probability that a randomly chosen bulb will last between 850 and 1050 hours? 83.8%

2) A survey showed that an average of 332 students at Logan High see a movie in a theater each month. The standard deviation is 16.

a) Label the mean and the correct value for each standard deviation mark on the curve.

b) On any given month, what is the probability that more than 348 students see a movie in a

theater?16%

c) What is the probability on any given month that between 300 and 348 students see a movie in a theater?81.6%

3) The test scores for an Algebra 2 math test are normally distributed with a mean of 75 and a standard deviation of 7.5.

a) Label the mean and the correct value for each standard deviation mark on the curve.

b) What is the range of the middle 68% of the students? 67.5% to 82.5%

c) The top 2.5% in the class scored above what value? 90

d) Where is the 50th Percentile?75

e) The 25th percentile is at 70 points and the 75th percentile is at 80 points. Mark the approximate location of these scores on the curve. Create a box and whisker plot under the normal curve.

f) The 90th percentile is at 85 points. If there are 36 students in class, how many students scored below 85 points? About 32 How many scored above 85 points? About 4

Extra Credit: Use what you know about the 90th percentile to find the score for the 10th percentile.