One
Choose the graph of a normal distribution. (1)
B
The graph below shows the normal distribution. Answer the question by manipulating the sliders for the mean (μ) and standard deviation (σ). (7)
What effect does a decrease in the standard deviation have on the graph?
The bell curve steepens.
Which of the following are properties of any normal distribution? Choose all that apply. (3)
The total area under the curve is 1.
The graph below shows the normal distribution. Answer the question by manipulating the sliders for the mean (μ) and standard deviation (σ). (6)
What effect does an increase in the mean have on the graph?
The bell curve moves horizontally right.
The histogram below shows the distribution of a sample of a random variable. Answer the questions below. (5)
Unimodal-Symmetric
Shoe sizes of adult men (US Sizes)
Suppose a distribution has the mean, median, and mode as shown below. Is the distribution normal?
The mean is 42, the median is 42, and the mode is 42.
A. Yes
B. No
C. Maybe?
C. Maybe?
Suppose a distribution has the mean, median, and mode as shown below. Is the distribution normal?
The mean is 11, the median is 15, and the mode is 11.
A. Yes
B. No
C. Maybe?
B. No
The histogram below shows the distribution of a sample of a random variable. Answer the questions below. (4)
Describe the shape of the distribution
Which random variable best matches the distribution?
Unimodal-Symmetric
Height of male adults
Find the z-score for the data point x given mean μ and standard deviation σ. Round to two decimal places as needed.
x = 2
μ=14
σ=7
-1.71
Below is a standard normal distribution. Find the area of the shaded region using a z-score table. Write the answer with four decimal places. (13)
.9616
The grades on a history exam were roughly normally distributed with an average of 78 and standard deviation of 3. Terry scored a 94 on the exam.
Find the z-score for Terry's exam grade. Round to two decimal places as needed.
5.33
The graphs of two normal distributions are shown below. Which distribution has the greater mean? Which distribution has the greater standard deviation? (11)
Distribution A has the greater mean and the greater standard deviation.
The grades on a history exam were roughly normally distributed with an average of 70 and standard deviation of 2. Angel scored a 96 on the exam.
Find the z-score for Angel's exam grade. Round to two decimal places as needed.
13
The scores on a standardized test are normally distributed with a mean of 479 and standard deviation of 8. Seth scored a 499 on the test.
Seth scored better than what percentage of test takers? Enter the percentage rounded to one decimal place. Round your z-score to two decimal places before finding your answer.
99.38%
Below is a normal distribution with μ=55 and σ=8. What is the area of the shaded region? Round your z-score to two decimal places before finding your answer. Write the answer with four decimal places. (14)
.9162
Find the z-score for the data point x given mean =μ and standard deviation σ. Round to two decimal places as needed.
x=35
μ=38
σ=2
-1.5
Below is a normal distribution with μ=25 and σ=3. What is the area of the shaded region? Round your z-score to two decimal places before finding your answer. Write the answer with four decimal places. (18)
.5
Below is a normal distribution with μ=33 and σ=10. What is the area of the shaded region? Round your z-score to two decimal places before finding your answer. Write the answer with four decimal places. (17)
.0808
Suppose the weights of watermelons are normally distributed. If 68% of the weights are between 16 and 18 pounds, what is the best estimate, in pounds, for the mean and standard deviation?
Mean = 17 lb
SD = 1 lb
Below is a normal distribution with μ=57 and σ=12. What is the area of the shaded region? Round your z-score to two decimal places before finding your answer. Write the answer with four decimal places. (12)
.1056