1) Find the missing parameter

1.mean 15, 30.15 %, above 50; what is the standard deviation
2.mean 75, 5.05% below 30; what is the standard deviation
3.standard deviation 9, 85.08% below 105: what is the mean
4.standard deviation 16.8, 15.62% above 18.3: what is the mean

Z = (raw score - mean)/standard deviation

Look up the percentage in a table in the back of your stat text labeled something like "areas under a normal distribution" to get your Z score value.

Insert the values into the equation above and solve for the unknown.

I hope this helps. Thanks for asking.

what is the probabilty of a sample of 25 houses will be tetween 145 and 160 days

To find the missing parameter in each of the given scenarios, we can use the z-score formula and properties of the standard normal distribution.

1) Given:
Mean = 15
Percentage above 50 = 30.15%

To find the standard deviation, we need to calculate the z-score corresponding to the given percentage. The formula for the z-score is:

z = (x - μ) / σ

where z is the z-score, x is the value we want to find the z-score for, μ is the mean, and σ is the standard deviation.

Let's denote the value we want to find the z-score for as Y.

Since the percentage is above 50, the z-score can be calculated as:

z = (50 - 15) / σ

We need to solve this equation for σ.

30.15% corresponds to a z-score of approximately 0.5206. So we have:

0.5206 = (50 - 15) / σ

Simplifying the equation:

0.5206σ = 35

Dividing both sides by 0.5206:

σ ≈ 67.19

Therefore, the standard deviation is approximately 67.19.

2) Given:
Mean = 75
Percentage below 30 = 5.05%

To find the standard deviation, we again need to calculate the z-score corresponding to the given percentage.

Since the percentage is below 30, the z-score can be calculated as:

z = (30 - 75) / σ

We need to solve this equation for σ.

5.05% corresponds to a z-score of approximately -1.8821. So we have:

-1.8821 = (30 - 75) / σ

Simplifying the equation:

-1.8821σ = -45

Dividing both sides by -1.8821:

σ ≈ 23.89

Therefore, the standard deviation is approximately 23.89.

3) Given:
Standard deviation = 9
Percentage below 105 = 85.08%

To find the mean, we need to calculate the z-score corresponding to the given percentage.

85.08% corresponds to a z-score of approximately -1.0369. We have:

-1.0369 = (105 - μ) / 9

Simplifying the equation:

-1.0369 * 9 = 105 - μ

-9.3321 = 105 - μ

Rearranging the equation:

μ = 105 - (-9.3321)

μ = 105 + 9.3321

μ ≈ 114.33

Therefore, the mean is approximately 114.33.

4) Given:
Standard deviation = 16.8
Percentage above 18.3 = 15.62%

To find the mean, we need to calculate the z-score corresponding to the given percentage.

15.62% corresponds to a z-score of approximately 1.0348. We have:

1.0348 = (x - 18.3) / 16.8

Simplifying the equation:

16.8 * 1.0348 = x - 18.3

17.03184 = x - 18.3

Rearranging the equation:

x = 18.3 + 17.03184

x ≈ 35.33

Therefore, the mean is approximately 35.33.

To find the missing parameter in each scenario, we need to use the concept of z-scores. A z-score measures the number of standard deviations a particular value is from the mean.

1) Find the missing standard deviation:

To find the missing standard deviation, we need to calculate the z-score for the given value (50) in relation to the mean (15) and the standard deviation. The z-score formula is:

z = (x - μ) / σ

where z is the z-score, x is the value in question, μ is the mean, and σ is the standard deviation.

In this case, we have:

z = (50 - 15) / σ = 30.15

To solve for σ, we can rearrange the formula:

σ = (50 - 15) / 30.15

Thus, the missing standard deviation is obtained by dividing the difference between the given value and the mean by the z-score.

2) Find the missing standard deviation:

Similarly, to find the missing standard deviation, we can use the z-score formula:

z = (x - μ) / σ

In this case, we have:

z = (30 - 75) / σ = -5.05

By rearranging the formula:

σ = (30 - 75) / -5.05

Hence, the missing standard deviation for this scenario is calculated by dividing the difference between the given value and the mean by the negative value of the z-score.

3) Find the missing mean:

To find the missing mean, we can use the z-score formula:

z = (x - μ) / σ

In this case, we have:

z = (105 - μ) / 9 = -85.08

By rearranging the formula:

-85.08 * 9 = 105 - μ

Simplifying further:

-765.72 = 105 - μ

Rearranging the equation:

μ = 105 - (-765.72)

Thus, the missing mean can be found by subtracting the product of the standard deviation and the negative z-score from the given value.

4) Find the missing mean:

Using the z-score formula:

z = (x - μ) / σ

In this case, we have:

z = (18.3 - μ) / 16.8 = 15.62

Rearranging the formula:

15.62 * 16.8 = 18.3 - μ

Simplifying further:

262.176 = 18.3 - μ

Rearranging the equation:

μ = 18.3 - 262.176

Thus, the missing mean can be found by subtracting the product of the standard deviation and the z-score from the given value.