Mathematics, 04.07.2020 04:01 aaliyah80

A normal population has a mean of 22 and a standard deviation of 5. 1. Compute the z value associated with 25.
2. What proportion of the population is between 22 and 25?
3. What proportion of the population is less than 18?

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Answer from: carson5238

Given Information:

Mean = μ = 22

Standard deviation = σ = 5

Required Information:

1. z-value = ?

2. P(22 < X < 25) = ?

3. P(X < 18) = ?

1. z-value = 0.6

2. P(22 < X < 25) = 22.58%

3. P(X < 18) = 21.19%

Step-by-step explanation:

What is Normal Distribution?

Normal Distribution is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability

1. We want to find out the z-value associated with 25

$P(X = 25) = P(Z = \frac{x - \mu}{\sigma} )\\\\P(X = 25) = P(Z = \frac{25 - 22}{5} )\\\\P(X = 25) = P(Z = \frac{3}{5} )\\\\P(X = 25) = P(Z = 0.6)\\\\$

Therefore, the z-value associated with X = 25 is 0.6

2. We want to find out the proportion of the population that is between 22 and 25.

$P(22 < X < 25) = P( \frac{x - \mu}{\sigma} < Z < \frac{x - \mu}{\sigma} )\\\\P(22 < X < 25) = P( \frac{22- 22}{5} < Z < \frac{25 - 22}{5} )\\\\P(22 < X < 25) = P( \frac{0}{5} < Z < \frac{3}{5} )\\\\P(22 < X < 25) = P( 0 < Z < 0.6 )\\\\P(22 < X < 25) = P( Z < 0.6 ) - P( Z < 0 ) \\\\$

The z-score corresponding to 0 is 0.50

The z-score corresponding to 0.6 is 0.7258

$P(22 < X < 25) = 0.7258 - 0.50 \\\\P(22 < X < 25) = 0.2258\\\\P(22 < X < 25) = 22.58 \%$

Therefore, the proportion of the population that is between 22 and 25 is 22.58%

3. We want to find out the proportion of the population that is less than 18

$P(X < 18) = P(Z < \frac{x - \mu}{\sigma} )\\\\P(X < 18) = P(Z < \frac{18 - 22}{5} )\\\\P(X < 18) = P(Z < \frac{-4}{5} )\\\\P(X < 18) = P(Z < -0.8)\\\\$

The z-score corresponding to -0.8 is 0.2119

$P(X < 18) = 0.2119\\\\P(X < 18) = 21.19 \%$

Therefore, the proportion of the population that is less than 18 is 21.19%

How to use z-table?

Step 1:

In the z-table, find the two-digit number on the left side corresponding to your z-score. (e.g 1.0, 2.2, 0.5 etc.)

Step 2:

Then look up at the top of z-table to find the remaining decimal point in the range of 0.00 to 0.09. (e.g. if you are looking for 0.6 then go for 0.00 column)

Step 3:

Finally, find the corresponding probability from the z-table at the intersection of step 1 and step 2.

Answer from: Quest

answer: $\frac{sin40^{\circ}}{x} = \frac{sin60^{\circ}}{12}$

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

$\frac{sin40^{\circ}}{x} = \frac{sin60^{\circ}}{12}$

which is the required equation for finding the value of x,

$\frac{x}{sin40^{\circ}}= \frac{12}{sin60^{\circ}}$

$x= 12\times \frac{sin40^{\circ}}{sin60^{\circ}}$

$x= 12\times 0.74222719896$

$x= 8.90672638762\approx 8.967$

Answer from: Quest

two data sets with the same median will not have the same varaibility

step-by-step explanation:

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A normal population has a mean of 22 and a standard deviation of 5. 1. Compute the z value associat...

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