Chapter 7: Q. 36 (page 429)

An unknown distribution has a mean of $100$ , a standard deviation of $100$ , and a sample size of $100$ . Let $X =$ one object of interest.
What is $P (Σ x > 9, 000)$ ?

Short Answer

Expert verified

The value of $P (X > 9000) = 0.8413$ .

The graph is

Step by step solution

Given Information

The mean is $100$ , Standard deviation is $100$ , and a sample size of 100.

And we need to find $P (Σ x > 9, 000)$ localid="1648807337983" $P (Σ x > 9, 000)$ .

Calculation

The information is,

$\sum X ~ N (n μ_{x}, \sqrt{n} σ_{x})$

$\sum X ~ N ((100) (100), (\sqrt{100}) (100))$

Now, we can find the probability that the sum of the $100$ values is greater than $9000$

$P (X > 9000) = P (Z > \frac{X - n μ_{x}}{\sqrt{n} σ_{x}})$

$= P (Z > \frac{9000 - 10000}{1000})$

$= P (Z > - 1)$

$P (X > 9000) = 0.8413$

The graph of the answer is

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An unknown distribution has a mean of $100$ , a standard deviation of $100$ , and a sample size of $100$ . Let $X =$ one object of interest.
What is $P (Σ x > 9, 000)$ ?

Short Answer

Step by step solution

Given Information

Calculation

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An unknown distribution has a mean of 100, a standard deviation of 100, and a sample size of 100. Let X=one object of interest.What is P(Σx>9,000)?

Short Answer

Step by step solution

Given Information

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Calculus

Probability and Statistics

Pure Maths

Decision Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

An unknown distribution has a mean of $100$ , a standard deviation of $100$ , and a sample size of $100$ . Let $X =$ one object of interest.
What is $P (Σ x > 9, 000)$ ?