Use the image to answer the question.
A solid distribution curve A, a dotted distribution curve B, and a dashed dotted distribution curve C are plotted on the first quadrant of a coordinate plane. All three curves are normal distribution curves.
Which curve has the lowest standard deviation?
(1 point)
Responses
A
A
B
B
C
C
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Question
The mean score on a particular test is 79 and the standard deviation is 5.5. What is the probability that a randomly selected test score is more than 90?(1 point)
Responses
34%
34%
5%
5%
95%
95%
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5%
The male shoe sizes within a community are normally distributed with a mean of μ=10
and a standard deviation of σ=1.5
. Apply the Empirical Rule to find the probability that a man will have a shoe size between 13 and 14.5.(1 point)
Responses
34%
34%
13.5%
13.5%
2.35%
A normal distribution has a mean of 645.33 and a standard deviation of 12.78. Approximately 68 percent of the data will lie between which two values?(1 point)
Responses
606.99 and 683.67
606.99 and 683.67
632.55 and 658.11
632.55 and 658.11
619.77 and 670.89
632.55 and 658.11
In a certain neighborhood, the average number of candies received while trick-or-treating is 50, with a standard deviation of 12. If Isaac received 40 candies, calculate his z-score to the nearest thousandth.(1 point)
Responses
0.833
0 point 8 3 3
−0.833
negative 0 point 8 3 3
0.300
0 point 3 0 0
−0.300
To calculate the z-score, we use the formula:
\[ z = \frac{(X - \mu)}{\sigma} \]
Where:
- X = value (In this case, Isaac's candy count which is 40)
- μ = mean (given as 50)
- σ = standard deviation (given as 12)
Plugging in the values, we get:
\[ z = \frac{(40 - 50)}{12} = \frac{-10}{12} \approx -0.833 \]
Therefore, the z-score to the nearest thousandth is approximately -0.833.
The number of books that high school students in the United States read in a year is normally distributed with a mean of 25 books and a standard deviation of 2.5 books. Complete the input for the spreadsheet program to calculate the probability that a high school student chosen at random will read more than 28 books in a year. Then identify this probability. Round the answers to the nearest tenth.
A B
1 Mean
2 Standard Deviation
3 x
4 Cumulative TRUE
5
=NormDist (B3, B1, B2, B4)
What is the probability that a high school student chosen at random will read more than 28 books in a year.
(1 point)
Responses
88.5%
88.5%
28%
28%
11.5%
Using the provided formula in the spreadsheet:
`=NormDist(28, 25, 2.5, TRUE)`
Calculating this in a spreadsheet would give the cumulative probability.
This would result in a probability of approximately 11.5% that a high school student chosen at random will read more than 28 books in a year.
Correct option:
11.5%