Calculation: Let ¯ X denote the average of 30 observations. Then ¯ X follows a normal distribution too, with a mean of μ=40 and a standard deviation σ √ n = 8 √ 30 ≈1.4606. So the standardisation of ¯ X yields P( ¯ X

Question

Calculation: Let 
¯
X
 denote the average of 30 observations.

Then 
¯
X
 follows a normal distribution too, with a mean of μ=40 and a standard deviation 
σ

√
n
=
8

√
30
≈1.4606.

So the standardisation of 
¯
X
 yields

P(
¯
X
<37)=P(
¯
X
−40

1.4606
<
37−40

1.4606
)=P(Z<−2.05)=P(Z>2.05)=0.02018.

Select "Continue" to continue.

BlackTom AI · Accepted Answer

The question presents a calculation involving the sampling distribution of the sample mean X̄ for 30 observations with μ = 40 and σ/√n = 8/√30 ≈ 1.4606. It then evaluates P(X̄ < 37) by standardizing to Z: (X̄ − 40) / 1.4606 < (37 − 40) / 1.4606 = −3 / 1.4606 ≈ −2.05. This corresponds to P(Z < −2.05), which is equal to P(Z > 2.05) due to symmetry. The computed value is approximately 0.02018, i.e., about 2.0%. The prompt then instructs to select “Continue” to proceed.

Option analysis:
- Option: "Continue" — This is the only choice presented. Given the workflow described, after performing the standardization and finding the probability P(X̄ < 37) ≈ 0.02018, the next instructed action is to proceed by selecting Continue. The reasoning behind this action rests on recognizing that the calculation step and the resulting probability are complete, and the prompt directs moving forward by clicking Continue.

In context, you can validate the intermediate steps: compute the standard error as 8/√30 ≈ 1.4606, compute the Z-score (37 − 40)/1.4606 ≈ −2.05, consult the standard normal distribution to obtain P(Z < −2.05) ≈ 0.02018, and then follow the instruction to continue. If any doubt remains about the numerical value, you could cross-check with a Z-table or a calculator, but the general procedure and the action to select Continue align with the given instruction.

2025-MS1004 practice quiz 6 -- optional homework -- for self-assessment

View Explanation

Log in for full answers

Similar Questions

In a consumer society, many adults channel creativity into buying things

Economic stress and unpredictable times have resulted in a booming industry for self-help products

People born without creativity never can develop it

A product has a selling price of $20, a contribution margin ratio of 40% and fixed cost of $120,000. To make a profit of $30,000. The number of units that must be sold is: Type the number without $ and a comma. Eg: 20000

Which of the following statement regarding cost is correct:

Under the assumptions used in cost-volume-profit analysis, as the activity increases:

The CVP and break-even analysis are supported by a range of important assumptions. Which of the following is not an assumption of the CVP:

The break-even point is that at which:

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler