According to the Empirical Rule, the probability that a selected dog of this breed weighs more than 161 pounds is about

Question

According to the Empirical​ Rule, the probability that a selected dog of this breed weighs more than 161 pounds is about

BlackTom AI · Accepted Answer

To approach this, recall the Empirical Rule (68-95-99.7) for a normal distribution: about 68% of data lie within one standard deviation of the mean, about 95% within two standard deviations, and about 99.7% within three standard deviations.
Option by option analysis:
Option 1: 32% — This would represent the total probability outside one standard deviation (both tails combined), since 68% lie within ±1 sd, leaving 32% outside. It does not correspond to the probability of a single tail (above mean +1 sd or below mean −1 sd) alone.
Option 2: 16% — This matches the probability in the upper tail above mean +1 sd (and symmetrically in the lower tail below mean −1 sd). If 161 pounds is exactly one standard deviation above the mean, then P(weight > 161) would be about 16%.
Option 3: 5% — This would correspond to a tail beyond roughly mean +2 sd (2.5% in one tail for a symmetric normal, rounding to 5% would be the total in both tails beyond ±2 sd, but not the single-tail value). It does not align with the 68-95-99.7 framework for the 161-pound threshold.
Option 4: 10% — This value does not align with the standard Empirical Rule breakdown for a single standard deviation increment or the typical tail proportions at common multiples of sd. It’s an inconsistent choice given the standard 1-sd and 2-sd intervals.
In summary, the Empirical Rule implies that about 16% of observations lie above mean + 1 sd (and 16% below mean − 1 sd). Since 161 pounds is positioned at mean + 1 sd, the correct interpretation is that roughly 16% of dogs weigh more than 161 pounds. Therefore, option 2 is the correct choice, and the other options misinterpret the tail probabilities or misplace them relative to the standard deviation thresholds.

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According to the Empirical Rule, the probability that a selected dog of this breed weighs more than 161 pounds is about

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251A-STATS-10-LEC-1 Quiz #6- Requires Respondus LockDown Browser

According to the Empirical​ Rule, the probability that a selected dog of this breed weighs more than 161 pounds is about

View Explanation

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Similar Questions

Suppose a population has probability distribution with a mean 𝜇 and a standard deviation 𝜎 . If a random sample of 100 measurements are taken from this population, you would expect very few of them to fall within 3 standard deviations of the mean. c07.p066.q001

The Empirical Rule states that for a bell-shaped distribution, approximately 95 percent of data should lie within:

Empirical Rule Q3 d) Find P(LB < Z< UB). Enter your answer to 4 decimal places.

Empirical Rule Q3 b) What is the numerical value for the upper bound (UB) of the interval? Enter your answer as a whole number.

Empirical Rule Q3 a) What is the numerical value for the lower bound (LB) of the interval? Enter your answer as a whole number.

Empirical Rule Q2 d) Find P(LB < Z< UB). Enter your answer to 4 decimal places.

Empirical Rule Q2 b) What is the numerical value for the upper bound (UB) of the interval? Enter your answer as a whole number.

Empirical Rule Q2 a) What is the numerical value for the lower bound (LB) of the interval? Enter your answer as a whole number.

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According to the Empirical Rule, the probability that a selected dog of this breed weighs more than 161 pounds is about