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.