Use Table A (or the equivalent technology) to find the value z of a standard Normal variable that is closest to having 25% of the observations falling above it.

Question

BlackTom AI · Accepted Answer

The task asks for the z-value on a standard normal distribution such that 25% of observations fall above it. In other words, find z where P(Z > z) = 0.25. This is equivalent to P(Z ≤ z) = 0.75 because the total area is 1.

Using the standard normal table or a calculator, the 0.75 quantile is about z = 0.674..., commonly rounded to 0.67. Therefore, the value that makes the upper tail 25% is around 0.67.

If the problem asks for the closest value, 0.67 is indeed a reasonable approximation.

Note: since there are no answer choices provided in the prompt, we can’t link to a specific option, but the computed z ≈ 0.6745.

Some potential misconceptions: thinking the cutoff corresponds to the lower tail (e.g., z negative) would yield more than 25% above, and selecting z = -0.67 would place 75% above, which is incorrect. Another point: rounding to 0.67 vs 0.68 slightly shifts the tail area; 0.6745 is the precise solution, so 0.67 is the closest commonly used two-decimal value.

STAT 1450.02 SP2025 (28132) Checkpoint 3.8

Use Table A (or the equivalent technology) to find the value z of a standard Normal variable that is closest to having 25% of the observations falling above it.

查看解析

登录即可查看完整答案

类似问题

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?

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?

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

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单