Write a percent between 25% and 50%.then write it as a decimal and as a fraction in simplest form

A manufacturer knows that their items have a normally distributed length, with a mean of 15.4 inches, and standard deviation of

Masteriza [31]

Answer:

0.9452 = 94.52% probability that their mean length is less than 16.8 inches.

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 establishes 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 15.4 inches, and standard deviation of 3.5 inches.

This means that $\mu = 15.4, \sigma = 3.5$

16 items are chosen at random

This means that $n = 16, s = \frac{3.5}{\sqrt{16}} = 0.875$

What is the probability that their mean length is less than 16.8 inches?

This is the p-value of Z when X = 16.8. So

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

By the Central Limit Theorem

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

$Z = \frac{16.8 - 15.4}{0.875}$

$Z = 1.6$

$Z = 1.6$ has a p-value of 0.9452.

0.9452 = 94.52% probability that their mean length is less than 16.8 inches.

5 0

3 years ago

Gina is a certain age (g). Gina's older sister is twice Gina's age. Gina's brother is half Gina's age. The sum of their ages is

aliina [53]

Answer:

Gina is 12 years old

Step-by-step explanation:

First, we will have to write these statements mathematically and then solve.

Let Gina's age be x, let Gina's brother's age be y and let Gina's sister's age be z.

The second statement"Gina's older sister is twice Gina's age" can be mathematically written as: z =2 x ---------------------------(1)

The next statement "Gina's brother is half Gina's age" can be mathematically written as y = $\frac{x}{2}$ ---------------------------------------(2)

Then the next statement "the sum of their ages is 42" can be mathematically written as: x + y + z = 42 ----------------------------(3)

We can now proceed to solve;

Substitute equation (1) and equation(2) into equation (3)

x + y + z = 42

x + $\frac{x}{2}$ + 2x = 42

Multiply through by 2

2x + x + 4x = 84

7x = 84

Divide both-side of the equation by 7

$\frac{7x}{7}$ = $\frac{84}{7}$

x = 12

Therefore, Gina is 12 years old

7 0

3 years ago

mr.ellis has started a vegetable garden.he bought 15 bags of soil and 3 bags of fertilizer for 282.72.he realized he didnt have

ANTONII [103]

The cost of each bag of soil is $ 16.25 and the cost of each bag of fertilizer is $ 12.99.

<h3>What is the linear system?</h3>

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Mr. Ellis has started a vegetable garden.

He bought 15 bags of soil and 3 bags of fertilizer for 282.72.

He realized he did not have enough supplies so he bought another 5 bags of soil and 2 bags of fertilizer for 107.23.

Let the cost of each bag of soil be x and the cost of a bag of fertilizer be y.

Then we have the linear equations,

15x + 3y = 282.72

5x + 2y = 107.23

On solving the equations 1 and 2, we have

x = 16.25 and y = 12.99

The cost of each bag of soil is $ 16.25 and the cost of each bag of fertilizer is $ 12.99.

More about the linear system link is given below.

brainly.com/question/20379472

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8 0

2 years ago

I need your help! Which one's are correct?!

dlinn [17]

Answer:

The first one and the last one

mark brainliest pls

8 0

2 years ago

Read 2 more answers

Which graph represents a function? A coordinate plane shows 4 points with the following coordinates: (negative 3, 3), (negative

Jet001 [13]

The ordered pair that represents a function is:

⇒ (-3, 3), (-2, -2), (1, 1), (2, -2)

<u>What are Coordinates?</u>

A pair of numbers that describe the exact position of a point on a cartesian plane by using horizontal and vertical lines are called the coordinates.

The given points are;

(-3, 3), (-3, -3), (-1, 1), (1, 4)

(-3, 3), (-2, -2), (1, 1), (2, -2)

(-3, 3), (-3, -3), (1, -4), (1, 1)

(-4, 4), (-4, 1), (-2, 1), (2, 1)

Now, For an ordered pair to be a function, either of the following must be true:

Each x-value has exactly one corresponding y-value.

More than one x-values have the same corresponding y-values.

And, If any of the following conditions is true, then the ordered pair is not a function,

One x-value has multiple corresponding y-values.

More than one x-values have multiple corresponding y-values.

From the given options, only ordered pair (-3, 3), (-2, -2), (1, 1), (2, -2) satisfies the condition to be a function.

Because none of its x-values have multiple corresponding y-values.

And, Other ordered pairs are either one-to-many or many-to-many.

So, The ordered pair that represents a function is:

⇒ (-3, 3), (-2, -2), (1, 1), (2, -2)

To learn more about ordered pairs visit:

brainly.com/question/19267542

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4 0

1 year ago