Mathematics, 22.04.2020 17:30 kamrulh278

If the mean GPA among students is 3.25 with a standard deviation of 1.75, and we select a random sample of 300 people, at what value for the sample mean would be greater than exactly 95% of possible sample means?

Answers: 3

Show answers

Answers

Answer from: samiyahwhite4792

X = 3.4161

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:

$\mu = 3.25, \sigma = 1.75, n = 300, s = \frac{1.75}{\sqrt{300}} = 0.101$

At what value for the sample mean would be greater than exactly 95% of possible sample means?

This is X when Z has a pvalue of 0.95. So X when Z = 1.645.

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

By the Central Limit Theorem

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

$1.645 = \frac{X - 3.25}{0.101}$

X - 3.25 = 1.645*0.101

X = 3.4161

Answer from: Quest

There is no graph ?

Answer from: Quest

a. turk and mcalister

b. howard, mission, and market

c. yes. since streets end some do not cross yet are not parallel to others. example: mcalister and 5th

step-by-step explanation:

parallel lines are lines which do not intersect ever and look a lot like railroad tracks. turk, mcalister and golden gate are examples of these.

intersect are streets which cross each other and a car on one can reach the other. howard, mission, and market intersect with 6th.

skew lines are lines which neither intersect nor are parallel. these lines exist here because some streets end and never intersect another like mcalister and 5th.

A. name the streets that are parallel to golden gate. b. name the streets that intersect 6th street.

Another question on Mathematics

Mathematics, 21.06.2019 13:30

Suppose that f(0) = −3 and f '(x) ≤ 8 for all values of x. how large can f(4) possibly be? solution we are given that f is differentiable (and therefore continuous) everywhere. in particular, we can apply the mean value theorem on the interval [0, 4] . there exists a number c such that

Answers: 1

Answer

Mathematics, 21.06.2019 16:30

What is the equation of a vertical line passing through the point (−5, −1)? y = −5 y = −1 x = −5 x = −1

Answers: 2

Answer

Mathematics, 21.06.2019 18:00

Simplify the expression. -2/5(10+15m-20n)

Answers: 1

Answer

Mathematics, 21.06.2019 19:30

What are the solutions to the following equation? |m| = 8.5 the value of m is equal to 8.5 and because each distance from zero is 8.5.