Mathematics, 22.04.2020 23:54 ggdvj9gggsc

According to an IRS study, it takes a mean of 330 minutes for taxpayers to prepare, copy, and electronically file a 1040 tax form. This distribution of times follows the normal distribution and the standard deviation is 80 minutes. A consumer watchdog agency selects a random sample of 40 taxpayers. What is the likelihood the sample mean is greater than 320 minutes?

Answers: 1

Show answers

Answers

Answer from: benjamenburton1

78.52% probability that the sample mean is greater than 320 minutes

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:

$\mu = 330, \sigma = 80, n = 40, s = \frac{80}{\sqrt{40}} = 12.65$

What is the likelihood the sample mean is greater than 320 minutes?

This is 1 subtracted by the pvalue of Z when X = 320. So

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

By the Central Limit Theorem

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

$Z = \frac{320 - 330}{12.65}$

Z = -0.79

Z = -0.79 has a pvalue of 0.2148

1 - 0.2148 = 0.7852

78.52% probability that the sample mean is greater than 320 minutes

Answer from: Quest

sadsadsadsad

step-by-step explanation:

Answer from: Quest

the answer would be d

straight away you can eliminate a and c because not all books contain a scientific skill because some may be fiction. c is also wrong because it saids that the only way children can learn is through books which is incorrect.

b is also wrong because reading can be a scientific skill but not always, therefore it is wrong which leaves you with d, the correct answer since it said that it can children learn.

hope this ! : 3

Another question on Mathematics

Mathematics, 21.06.2019 15:00

Idon’t understand this.. will someone ? will mark brainliest along with 20 points.

Answers: 1

Answer

Mathematics, 21.06.2019 17:20

Read the equations in the table below. then drag a description of the situation and a table to represent each equation. indicate whether each of the relationships is proportional or non-proportional.

Answers: 1

Answer

Mathematics, 21.06.2019 19:30

Plz.yesterday, the snow was 2 feet deep in front of archie’s house. today, the snow depth dropped to 1.6 feet because the day is so warm. what is the percent change in the depth of the snow?

Answers: 1

Answer

Mathematics, 21.06.2019 19:30

Ariel is working at a meat packing plant for 5 nights a week. her regular wage is $11 an hour. she earns tine and a half for any overtime hours. this week she worked 9 hours of over time .how much will ariel earn for overtime this week ?

Answers: 1

Answer

You know the right answer?

According to an IRS study, it takes a mean of 330 minutes for taxpayers to prepare, copy, and electr...

Questions