Mathematics, 06.06.2020 23:57 thesusan7494

If the average ago of retirement for a random sample of 87 retired persons is 66 years with a standard deviation of 2 years. a. b. c. d. e.f. g. Find the probability of finding a random sample of 87 retired people in which the average age of retirement is 66.5 or more. Find all values to 3 decimal places.

Answers: 2

Show answers

Answers

0.01 = 1% probability of finding a random sample of 87 retired people in which the average age of retirement is 66.5 or more.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

$\mu = 66, \sigma = 2, n = 87, s = \frac{2}{\sqrt{87}} = 0.214$

Find the probability of finding a random sample of 87 retired people in which the average age of retirement is 66.5 or more.

This probability is 1 subtracted by the pvalue of Z when X = 66.5. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{66.5 - 66}{0.214}$

Z = 2.336

Z = 2.336 has a pvalue of 0.99.

1 - 0.99 = 0.01

0.01 = 1% probability of finding a random sample of 87 retired people in which the average age of retirement is 66.5 or more.

Answer from: Quest

saving = more money

step-by-step explanation:

if you have 100 bucks, and you want to buy a candy bar, even if you have one at home, if you choose not to buy it, you save.

~courtney

Answer from: Quest

The linear equation is: y=ax+b

Another question on Mathematics

Mathematics, 21.06.2019 22:00

Which statements describe the solutions to the inequality x< -20 check all that apply. there are infinite solutions. each solution is negative. each solution is positive. the solutions are both positive and negative. the solutions contain only integer values. the solutions contain rational number values.

Answers: 1

Answer

Mathematics, 21.06.2019 23:30

Find │7│. a. 1 over 7 b. –7 c. 7 asap i always mark brailiest who me so

Answers: 1

Answer

Mathematics, 22.06.2019 01:00

What is the value of the discriminant, b2 ? 4ac, for the quadratic equation 0 = x2 ? 4x + 5, and what does it mean about the number of real solutions the equation has?

Answers: 3

Answer

Mathematics, 22.06.2019 02:30

Which statement best explains whether the table represents a linear or nonlinear function? input (x) output (y) 2 5 4 10 6 15 8 20 it is a linear function because the input values are increasing. it is a nonlinear function because the output values are increasing. it is a linear function because there is a constant rate of change in both the input and output. it is a nonlinear function because there is a constant rate of change in both the input and output.

Answers: 3

Answer

You know the right answer?

If the average ago of retirement for a random sample of 87 retired persons is 66 years with a standa...

Questions

Mathematics, 22.04.2021 23:30

Pls pls pls help me giving brainlist ...