Question
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Part 1
The cost of movie tickets at several movie theaters is normally distributed with a mean ticket price of $10 and a standard deviation of $0.50. Kenji bought a movie ticket for $9.25. Explain and correct the error in finding the z-score.
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Part 1
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.
The formula for the z-score is incorrect. It should be zequalsStartFraction data value minus mean Over standard deviation EndFraction
equalsStartFraction $ 9.25 minus $ 10 Over $ 0.5 EndFraction
equals
enter your response here.
(Type an integer or decimal rounded to one decimal place as needed.)
B.
The formula for the z-score is incorrect. It should be zequalsStartFraction standard deviation Over mean minus data value EndFraction
equalsStartFraction $ 0.5 Over $ 10 minus $ 9.25 EndFraction
equals
g.
(Type an integer or decimal rounded to one decimal place as needed.)
C.
The computation is incorrect. The correct computation is zequalsStartFraction $ 10 minus $ 9.25 Over $ 0.5 EndFraction
equals
enter your response here.
(Type an integer or decimal rounded to one decimal place as needed.)
D.
The z-score should have units of dollars. The correct answer is zequals$1.5.
Part 1
The cost of movie tickets at several movie theaters is normally distributed with a mean ticket price of $10 and a standard deviation of $0.50. Kenji bought a movie ticket for $9.25. Explain and correct the error in finding the z-score.
Question content area bottom
Part 1
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.
The formula for the z-score is incorrect. It should be zequalsStartFraction data value minus mean Over standard deviation EndFraction
equalsStartFraction $ 9.25 minus $ 10 Over $ 0.5 EndFraction
equals
enter your response here.
(Type an integer or decimal rounded to one decimal place as needed.)
B.
The formula for the z-score is incorrect. It should be zequalsStartFraction standard deviation Over mean minus data value EndFraction
equalsStartFraction $ 0.5 Over $ 10 minus $ 9.25 EndFraction
equals
g.
(Type an integer or decimal rounded to one decimal place as needed.)
C.
The computation is incorrect. The correct computation is zequalsStartFraction $ 10 minus $ 9.25 Over $ 0.5 EndFraction
equals
enter your response here.
(Type an integer or decimal rounded to one decimal place as needed.)
D.
The z-score should have units of dollars. The correct answer is zequals$1.5.
Answers
Answered by
GPT-4o mini
To find the z-score correctly, we need to use the appropriate formula for z-score calculation:
\[ z = \frac{x - \mu}{\sigma} \]
where:
- \( x \) is the data value (in this case, Kenji's ticket price of $9.25),
- \( \mu \) is the mean (which is $10),
- \( \sigma \) is the standard deviation (which is $0.50).
Let's examine each option provided:
**A.** This option describes the correct formula. Let's compute the z-score using it.
\[
z = \frac{9.25 - 10}{0.5} = \frac{-0.75}{0.5} = -1.5
\]
So option A is correct in terms of the formula and calculation.
**B.** This option incorrectly alters the formula as it implies using the standard deviation in the numerator and rearranging the formula, which is not correct.
**C.** This option also misrepresents the calculation by swapping the subtraction order. The correct calculation is \( 9.25 - 10 \), not \( 10 - 9.25 \).
**D.** This option incorrectly states that the z-score has units of dollars and gives an incorrect value for the z-score.
The correct choice is **A**, and would be completed as follows:
\[
z = \frac{9.25 - 10}{0.5} = -1.5
\]
Thus, the correct answer is:
**A.** \( z = -1.5 \) (rounded to one decimal place).
\[ z = \frac{x - \mu}{\sigma} \]
where:
- \( x \) is the data value (in this case, Kenji's ticket price of $9.25),
- \( \mu \) is the mean (which is $10),
- \( \sigma \) is the standard deviation (which is $0.50).
Let's examine each option provided:
**A.** This option describes the correct formula. Let's compute the z-score using it.
\[
z = \frac{9.25 - 10}{0.5} = \frac{-0.75}{0.5} = -1.5
\]
So option A is correct in terms of the formula and calculation.
**B.** This option incorrectly alters the formula as it implies using the standard deviation in the numerator and rearranging the formula, which is not correct.
**C.** This option also misrepresents the calculation by swapping the subtraction order. The correct calculation is \( 9.25 - 10 \), not \( 10 - 9.25 \).
**D.** This option incorrectly states that the z-score has units of dollars and gives an incorrect value for the z-score.
The correct choice is **A**, and would be completed as follows:
\[
z = \frac{9.25 - 10}{0.5} = -1.5
\]
Thus, the correct answer is:
**A.** \( z = -1.5 \) (rounded to one decimal place).