after recording the pizza delivery times for two different pizza shops, you conclude that one pizza shop has a mean delivery time of 45 minutes with a standard deviation of 4 minutes. the other shop has a mean delivery time of 43 minutes with a standard deviation of 22 minutes. interpret these figures. if you liked the pizzas from both shops equally well, which one would you order from? why?

interpret these figures. choose the correct answer below.

a. both the means and the variations are nearly equal.
b. the means are nearly equal, but the variation is significantly greater for the second shop than for the first.
c. the means are nearly equal, but the variation is significantly lower for the second shop than for the first.
d. the variations are nearly equal, but the mean is greater for the first shop than for the second.

Question

after recording the pizza delivery times for two different pizza shops, you conclude that one pizza shop has a mean delivery time of 45 minutes with a standard deviation of 4 minutes. the other shop has a mean delivery time of 43 minutes with a standard deviation of 22 minutes. interpret these figures. if you liked the pizzas from both shops equally well, which one would you order from? why?

interpret these figures. choose the correct answer below.

a. both the means and the variations are nearly equal.
b. the means are nearly equal, but the variation is significantly greater for the second shop than for the first.
c. the means are nearly equal, but the variation is significantly lower for the second shop than for the first.
d. the variations are nearly equal, but the mean is greater for the first shop than for the second.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Measures of Center" ], "new_concepts": [ "Standard Deviation Interpretation", "Data Variability Analysis" ], "current_concepts": [ "Measures of Center", "Standard Deviation Interpretation", "Data Variability Analysis" ] } ## Identify the given statistics Using the *Measures of Center* knowledge point $$ \begin{aligned} &\text{Shop 1: } \mu_1 = 45\text{ minutes},\quad \sigma_1 = 4\text{ minutes}\ &\text{Shop 2: } \mu_2 = 43\text{ minutes},\quad \sigma_2 = 22\text{ minutes} \end{aligned} $$ ## Compare the means of both shops The mean delivery times are $45\text{ minutes}$ and $43\text{ minutes}$. Since the difference is only $2\text{ minutes}$, the means are nearly equal. ## Compare the variations of both shops The standard deviation measures the variation or spread of the delivery times. - Shop 1 has a standard deviation of $\sigma_1 = 4\text{ minutes}$. - Shop 2 has a standard deviation of $\sigma_2 = 22\text{ minutes}$. Comparing these values: $$ 22\text{ minutes} \gg 4\text{ minutes} $$ Thus, the variation is significantly greater for the second shop than for the first shop. ## Match with the correct option Combining our findings: - The means are nearly equal ($45$ vs. $43$ minutes). - The variation is significantly greater for the second shop ($22$ minutes) than for the first shop ($4$ minutes). This matches option B.

(A) Both the means and the variations are nearly equal.

(B) The means are nearly equal, but the variation is significantly greater for the second shop than for the first.

(C) The means are nearly equal, but the variation is significantly lower for the second shop than for the first.

(D) The variations are nearly equal, but the mean is greater for the first shop than for the second.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Standard Deviation Interpretation" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given statistics

Compare the means of both shops

Compare the variations of both shops

Match with the correct option

Answer: