Mathematics, 27.03.2020 18:49 lololololol16

The weights of college football players follows a normal distribution with mean 225 pounds and standard deviation 23 pounds. A random sample of 25 college football players is taken and the sample mean (Ybar) is computed. Calculate the following:

1. the mean of Ybar
2. the standard deviation of Ybar
3. the probability that Ybar will be greater than 235 pounds
4. the probability that the weight of a single randomly selected college football player will be greater than 235 pounds

Answers: 3

Show answers

Answers

Answer from: bandchick527

1) 225 pounds

2) 4.6 pounds

3) 1.50% Ybar will be greater than 235 pounds

4) 33.36% probability that the weight of a single randomly selected college football player will be greater than 235 pounds

Step-by-step explanation:

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:

$\mu = 225, \sigma = 23, n = 25, s = \frac{25}{\sqrt{25}} = 4.6$

1. the mean of Ybar

By the Central Limit Theorem, 225 pounds

2. the standard deviation of Ybar

By the Central Limit Theorem, 4.6 pounds

3. the probability that Ybar will be greater than 235 pounds

This is 1 subtracted by the pvalue of Z when X = 235. So

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

By the Central Limit Theorem

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

$Z = \frac{235 - 225}{4.6}$

Z = 2.17

Z = 2.17 has a pvalue of 0.9850

1 - 0.9850 = 0.0150

1.50% Ybar will be greater than 235 pounds

4. the probability that the weight of a single randomly selected college football player will be greater than 235 pounds

This is 1 subtracted by the pvalue of Z when X = 235. So

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

$Z = \frac{235 - 225}{23}$

Z = 0.43

Z = 0.43 has a pvalue of 0.6664

1 - 0.6664 = 0.3336

33.36% probability that the weight of a single randomly selected college football player will be greater than 235 pounds

Answer from: Quest

150.6

all i did was i multiplied 5.02 by 30

Answer from: Quest

is there supposed to be a diagram or a graph for this one? ?

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 15:00

Asmall foreign car gete 42 miles per gallon and user 35 gallons on a trip.gasoline costs $1.05 per gallon.what was the cost of gasoline per mile driver?

Answers: 3

Answer

Mathematics, 21.06.2019 22:10

Given: ae ≅ ce ; de ≅ be prove: abcd is a parallelogram. we have that ab || dc. by a similar argument used to prove that △aeb ≅ △ced, we can show that △ ≅ △ceb by. so, ∠cad ≅ ∠ by cpctc. therefore, ad || bc by the converse of the theorem. since both pair of opposite sides are parallel, quadrilateral abcd is a parallelogram.

Answers: 1

Answer

Mathematics, 21.06.2019 22:30

At the beginning of year 1, carlos invests $600 at an annual compound interest rate of 4%. he makes no deposits to or withdrawals from the account. which explicit formula can be used to find the account's balance at the beginning of year 5? what is, the balance?

Answers: 2

Answer

Mathematics, 21.06.2019 23:30

Maren is buying carpet for her rectangular living room. the room is 4.8 yards wide and 5.2 yards long. how much carpet does she need to buy? enter your answer as a decimal in the box. yd2

Answers: 1

Answer

You know the right answer?

The weights of college football players follows a normal distribution with mean 225 pounds and stand...

Questions

Mathematics, 14.02.2021 23:30

P-q:3::2q:7, then express "q" in terms of "p"....

Mathematics, 14.02.2021 23:30

What is the sum of the third and ninth square numbers?...