Mathematics, 08.04.2020 01:35 Anybody6153

In a study reported in the Flurry Blog on Oct. 29, 2012, the mean age of tablet users was 34 yrs, with a standard deviation of 15 years. Assuming a normal distribution, what is the approximate probability of picking a random sample of 40 tablet users with a mean age between 31 and 35 yrs?

Answers: 1

Show answers

Answers

Answer from: laskew37221

55.90% probability of picking a random sample of 40 tablet users with a mean age between 31 and 35 yrs

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 problem, we have that:

$\mu = 34, \sigma = 15, n = 40, s = \frac{15}{\sqrt{40}} = 2.37$

Assuming a normal distribution, what is the approximate probability of picking a random sample of 40 tablet users with a mean age between 31 and 35 yrs?

This is the pvalue of Z when X = 35 subtracted by the pvalue of Z when X = 31.

X = 35

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

By the Central Limit Theorem

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

$Z = \frac{35 - 34}{2.37}$

Z = 0.42

Z = 0.42 has a pvalue of 0.6628

X = 31

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

$Z = \frac{31 - 34}{2.37}$

Z = -1.26

Z = -1.26 has a pvalue of 0.1038

0.6628 - 0.1038 = 0.5590

55.90% probability of picking a random sample of 40 tablet users with a mean age between 31 and 35 yrs

Answer from: Quest

step-by-step explanation:

an equation by definition has to have two or more variables (x and 2 in this case)

Answer from: Quest

Okay so n is going to represent our first number. since the second number of five times greater than n, the second number will be represented as 5n. for us to figure out the two numbers we need to have the value of n first. this is going to be done by adding the two numbers together, n and 5n. it can be simplified as 6n, which the problem states is equal to 72. divide 72 by 6n and you can solve for n. n+5n=726n=72n=(72/6)n=12 now that we know the value of n, we have to multiply 5 times 12 which equals 60. so our two numbers/integers are 12 and 60