the perimeter of a rectangle is 54 meters. one side is 3 meters less than four times the length of the other side.

The mean height of a Clydesdale horse is 72 inches with a standard deviation of 1.2 inches. What is the probability that a Clyde

Lubov Fominskaja [6]

Answer:

0.0062

Step-by-step explanation:

Given that:

Mean (μ) = 72 inches, Standard deviation (σ) = 1.2 inches.

The z score is a measure in statistics is used to determine by how many standard deviation the raw score is above or below the mean. If the raw score is above the mean, the z score is positive and if the raw score is below the mean, the z score is negative.

The z score is given as:

$z=\frac{x-\mu}{\sigma}$

For Clydesdale is greater than 75 inches tall, x = 75 inches, the z score is:

$z=\frac{x-\mu}{\sigma}=\frac{75-72}{1.2} =2.5$

The probability that a Clydesdale is greater than 75 inches tall = P(X > 75) = P(Z > 2.5) = 1 - P(Z < 2.5) = 1 - 0.9938 = 0.0062 = 0.62%

The probability that a Clydesdale is greater than 75 inches tall is 0.62%

3 0

4 years ago

Parts being manufactured at a plant are supposed to weigh 65 grams. Suppose the distribution of weights has a Normal distributio

andrew-mc [135]

Answer:

0.64%.

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 normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, 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.

Mean of 75 grams and a standard deviation of 22 grams.

This means that $\mu = 75, \sigma = 22$

Sample of 144:

This means that $n = 144, s = \frac{22}{\sqrt{144}} = 1.8333$

More than 80 or less than 70:

Both are the same distance from the mean, so we find one probability and multiply by 2.

The probability that it is less than 70 is the pvalue of Z when X = 70. So

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

By the Central Limit Theorem

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

$Z = \frac{70 - 75}{1.8333}$

$Z = -2.73$

$Z = -2.73$ has a pvalue of 0.0032

2*0.0032 = 0.0064.

0.0064*100% = 0.64%

The probability is 0.64%.

3 0

3 years ago

Khalil has 13.5 M of lanyard he needs to cut the lanyards into pieces that are 90 cm long how many full-length pieces of a lanya

Dmitry [639]

We have been given that Khalil has 13.5 M of lanyard. He needs to cut the lanyards into pieces that are 90 cm long. We are asked to find the number of full-length pieces of a lanyard will Khalil be able to cut.

First of all, we will convert 13.5 meter into cm.

1 meter = 100 cm

13.5 meters = 13.5*100 = 1350 cm.

Now we will divide 1350 by 90 to find number of pieces of lanyard that can be cut from 1350 cm.

$\text{Number of full-length pieces of a lanyard}=\frac{1350}{90}$

$\text{Number of full-length pieces of a lanyard}=15$

Therefore, Khalil will be able to cut 15 full-length pieces of a lanyard.

3 0

3 years ago

(4x^y-4)3<br> Simplify please

pashok25 [27]

Answer:

12x^y-12

Step-by-step explanation:

Multiply 3 by 4

12x^y-4⋅3

12x^y-12

4 0

3 years ago

Jasmine wants to earn $2,000 in simple interest through a

Ierofanga [76]

Answer:

$10000

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 5%/100 = 0.05 per year,

then, solving our equation

P = 2000 / ( 0.05 × 4 ) = 10000

P = $ 10,000.00

The principal required to

accumulate interest of $ 2,000.00

on a rate of 5% per year for 4 years is $ 10,000.00.

3 0

3 years ago