Mathematics, 20.03.2020 19:03 dari122223

Suppose the horses in a large stable have a mean weight of 992lbs, and a standard deviation of 141lbs. What is the probability that the mean weight of the sample of horses would differ from the population mean by less than 13lbs if 37 horses are sampled at random from the stable? Round your answer to four decimal places.

Answers: 3

Show answers

Answers

0.4246 = 42.46% probability that the mean weight of the sample of horses would differ from the population mean by less than 13lbs if 37 horses are sampled at random from the stable

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 can be 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 random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sample means with size n of at least 30 can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 992, \sigma = 141, n = 37, s = \frac{141}{\sqrt{37}} = 23.18$

What is the probability that the mean weight of the sample of horses would differ from the population mean by less than 13lbs if 37 horses are sampled at random from the stable?

This is the pvalue of Z when X = 992 + 13 = 1005 subtracted by the pvalue of Z when X = 992 - 13 = 979.

X = 1005

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

By the Central Limit Theorem

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

$Z = \frac{1005 - 992}{23.18}$

Z = 0.56

Z = 0.56 has a pvalue of 0.7123

X = 979

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

$Z = \frac{979 - 992}{23.18}$

Z = -0.56

Z = -0.56 has a pvalue of 0.2877

0.7123 - 0.2877 = 0.4246

0.4246 = 42.46% probability that the mean weight of the sample of horses would differ from the population mean by less than 13lbs if 37 horses are sampled at random from the stable

Answer from: Quest

hi there!

the answer will be d: 2

Answer from: Quest

the system of inequalities is

$y> (1/3)x$

$y\leq-x+4$

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

$m=y/x=1/3$

the equation of the dashed line is

$y=(1/3)x$

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

$y> (1/3)x$

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

$m=(4-0)/(0-4)=-1$

the equation of the solid line is

$y=-x+4$

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

$y\leq-x+4$

step 3

the system of inequalities is

$y> (1/3)x$

$y\leq-x+4$

Another question on Mathematics

Mathematics, 21.06.2019 17:00

Determine the fraction of total interest owed. after the fourth month of a 12-month loan: the numerator is: {(n + ) + (n + ) + (n + ) + (n + )} = , and the denominator is: {(n) + (n + 1) + + (n + )} = . therefore, the fraction is numerator/denominator (to the nearest tenth) =

Answers: 1

Answer

Mathematics, 21.06.2019 17:30

During a bike challenge riders have to collect various colored ribbons each 1/2 mile they collect a red ribbon each eighth mile they collect a green ribbon and each quarter mile they collect a blue ribbion wich colors of ribion will be collected at the 3/4 markrer

Answers: 3

Answer

Mathematics, 21.06.2019 20:40

If the endpoints of the diameter of a circle are (8, 6) and (2,0), what is the standard form equation of the circle? a) (x + 5)2 + (y + 3)2 = 18 (x + 5)2 + (y + 3)2 = 3.72 (x - 5)2 + (y - 3)2 = 18 d) (x - 5)2 + (y - 3)2 = 32

Answers: 1

Answer

Mathematics, 21.06.2019 22:30

The given diagram shows the parts of a right triangle with an altitude to the hypotenuse. using the two given measures, find the other four.

Answers: 1

Answer

You know the right answer?

Suppose the horses in a large stable have a mean weight of 992lbs, and a standard deviation of 141lb...

Questions

Mathematics, 27.01.2020 18:31

Aleena has a 1-gallon watering can that is full of water. she uses 3/8gallon to water her roses and 1/3gallon to water her geraniums. how much water d...