题目

Problem

The probability that a person completes a particular task in less than 15 minutes is 0.4 Jeffrey selects 20 people at random and asks them to complete the task. The random variable, $X$ , represents the number of people who complete the task in less than 15 minutes.

(a) Find $P(5 \leqslant X < 8)$

(3)

Mia takes a random sample of 140 people. Using a normal approximation, the probability that fewer than $n$ of these 140 people complete the task in less than 15 minutes is 0.0239 to 4 decimal places.

(b) Find the value of $n$ Show your working clearly.

(6)

(Total for Question 4 is 9 marks)

题目中文翻译

一个人完成某项任务少于 15 分钟的概率为 0.4。 Jeffrey 随机抽取 20 个人并要求他们完成该任务。随机变量 $X$ 表示在少于 15 分钟内完成任务的人数。

(a) 求 $P(5 \leqslant X < 8)$ 。

Mia 随机抽取 140 个人。使用正态近似，这 140 个人中少于 $n$ 个人在少于 15 分钟内完成任务的概率为 0.0239，精确到 4 位小数。

(b) 求 $n$ 的值。清楚展示你的计算过程。

（第 4 题共 9 分）

IAL 2022 Oct S2 Q4

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