The mean height of a bull population is 150cm. The population shows a normal distribution with a standard deviation of 7cm. What will be the maximum height of bulls that are within 2 standard deviations of the mean?

Question

The mean height of a bull population is 150cm. The population shows a normal distribution with a standard deviation of 7cm. What will be the maximum height of bulls that are within 2 standard deviations of the mean?

BlackTom AI · Accepted Answer

Question restatement: The mean height of a bull population is 150 cm. The population shows a normal distribution with a standard deviation of 7 cm. What will be the maximum height of bulls that are within 2 standard deviations of the mean?

Answer options:
- 143 cm
- 171 cm
- 164 cm
- 157 cm

Option-by-option analysis:
Option 1: 143 cm. This value is 7 cm below the mean, i.e., mean − 1 SD (150 − 7 = 143). Being at −1 SD, it lies within 2 SDs, but the question asks for the maximum height within 2 SDs, not a point at another percentile. This option incorrectly seeks the lower bound at −1 SD, while the maximum within the 2-SD interval is higher.
Option 2: 171 cm. This is 21 cm above the mean, which corresponds to +3 SDs (since 3 × 7 = 21). Heights beyond +2 SD (which is 164 cm) are outside the specified range, so 171 cm is not within 2 standard deviations of the mean. This option overestimates the upper limit.
Option 3: 164 cm. This value equals the mean plus 2 SDs (150 + 2 × 7 = 164). It represents the upper bound of the interval from mean − 2 SD to mean + 2 SD. Therefore, 164 cm is the maximum height that still lies within 2 standard deviations of the mean.
Option 4: 157 cm. This is 1 SD above the mean (150 + 7 = 157). While it is within 2 SDs, it is not the maximum height within that range. The question asks for the maximum height within the 2-SD interval, so this is too low.

Summary: The 2-SD interval around the mean is from 150 − 2×7 = 136 cm to 150 + 2×7 = 164 cm. Among the options, 164 cm is the highest value still inside this interval, whereas the other options either lie outside the 2-SD range or are not the maximal value within it.

AGRI10051_2025_SM2 Supplementary or Special Exam: Genetics for Agriculture (AGRI10051_2025_SM2)- Requires Respondus LockDown Browser

The mean height of a bull population is 150cm. The population shows a normal distribution with a standard deviation of 7cm. What will be the maximum height of bulls that are within 2 standard deviations of the mean?

View Explanation

Log in for full answers

Similar Questions

X~N(3, 1) and Y~N(3, 2), then

Question at position 50 A soft-drink machine can be regulated so that it discharges an average of ? oz per cup. If the ounces of fill are Normally distributed with a standard deviation of 0.4 oz, what should ? be set at so that 98% of the 6-oz cups will not overflow?6.606.826.006.185.18

In a normal distribution where X ~N(0,1) , approximately what is the probability that X is between -1 and 0.

Suppose that the number of credit hours a student takes follows a normal distribution with a mean of 17 credit hours and a standard deviation of 2 credit hours. A normal course load is between 12 and 19 hours. What proportion of students have a normal course load?

Is BaP response-frequency approximately normally distributed with respect to log(dose)?

Question at position 4 ________ is the continuous probability distribution used most often for economics and business applications.Normal probability distributionExponential distributionUniform distributionIncremental distribution

More Practical Tools for International Students

Exam Browser Assistant

Stylized Writing Assistant

Plagiarism Checker Assistant

Citation Assistant

In-Class Translation Assistant

Class Notes Assistant

Quiz Search Assistant

Past Exam Questions by School

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler