Problems of normal distributions can be solved using the z-score formula, which for a measure X, in a distribution with mean $\mu$ and standard deviation $\sigma$ , is given by:

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

It measures how many standard deviations the measure is from the mean.
Each z-score has an associated p-value, which is the percentile.

The normal distribution is symmetric, which means that the middle 95% is between the <u>2.5th percentile and the 97.5th percentile</u>.
The 2.5th percentile is Z with a p-value of 0.025, thus Z = -1.96.
The 97.5th percentile is Z with a p-value of 0.975, thus Z = 1.96.
Thus, the value of Z is 1.96.

A similar problem is given at brainly.com/question/16965597

7 0

1 year ago

What is the value of x in the triangle?

yulyashka [42]

<h3>Answer: C) x = 13</h3>

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Work Shown:

We have a right triangle with legs a = 5 and b = 12. The hypotenuse is c = x which is unknown for now.

Use the pythagorean theorem to find x.

a^2 + b^2 = c^2

5^2 + 12^2 = x^2

25 + 144 = x^2

169 = x^2

x^2 = 169

x = sqrt(169) .... apply the square root to both sides

x = 13

4 0

2 years ago

Find the volume of the cylinder. Use 3.14 for pie

Rudik [331]

Volume of a cylinder formula is
$v = \pi {r}^{2} \times h$
$v = 3.14 \times {3}^{2} \times 12$

3 0

3 years ago

What's a real world problem involving a percent greater then 100%

AveGali [126]

Buying something that costs more than $1.00 can be an example.

8 0

2 years ago