If
𝑋
∼
𝑁
(
5
,
2
)
, then what code will calculate
𝑃
(
𝑋

1
)
?

Question

If 
𝑋
∼
𝑁
(
5
,
2
)
, then what code will calculate
𝑃
(
𝑋
>
1
)
?

BlackTom AI · Accepted Answer

We begin by restating the problem: X is distributed as N(5, 2) and we want P(X > 1).

First, clarify the notation: N(μ, σ^2) means the mean is μ and the variance is σ^2. Here the second parameter is 2, so the standard deviation is sqrt(2).

To compute P(X > 1) using the normal distribution, we can use the cumulative distribution function (CDF) via pnorm in R-like syntax. P(X > 1) = 1 - P(X ≤ 1) = 1 - pnorm(1, mean = 5, sd = sqrt(2)).

Option analysis:
- The expression 1 - pnorm(1, 5, sqrt(2)) exactly represents P(X > 1) for X ~ N(5, 2), since pnorm(1, 5, sqrt(2)) computes P(X ≤ 1) with the specified mean and standard deviation, and subtracting from 1 yields the tail probability.

Why this is correct: using the standard approach for a normal variable, convert the tail probability into the complement of the CDF at the point 1, applying the correct mean (5) and standard deviation (sqrt(2)). Numerically, z = (1 - 5) / sqrt(2) = -4 / 1.414... ≈ -2.828, so P(X > 1) ≈ Φ(2.828) ≈ 0.9977, which aligns with the complement calculation 1 - Φ(-2.828).

Potential confusion to avoid: if someone misinterprets the second parameter as the standard deviation, that would lead to an incorrect value only if the parameter usage differs from N(μ, σ^2). Here the expression uses sd = sqrt(2) explicitly, which is consistent with the standard deviation being the square root of the variance 2.

In summary, the given option 1-pnorm(1,5,sqrt(2)) is the correct formulation for P(X > 1) when X ~ N(5, 2).

DATA1001/1901 (ND) Evaluate Quiz 4

If 𝑋 ∼ 𝑁 ( 5 , 2 ) , then what code will calculate 𝑃 ( 𝑋 > 1 ) ?

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