A supervisor finds the mean number of miles that the employees in a department live from work. He finds x Overbar = 29 and s = 3.6. Which mileage is within a z-score of 1.5?
21 miles
24 miles
36 miles
41 miles
3.6 * 1.5 = 5.4
29 ± 5.4 = ?
A supervisor finds the mean number of miles that the employees in a department live from work. He finds x Overbar = 29 and s = 3.6. Which mileage is within a z-score of 1.5?
36 miles
Well, if we know that the mean number of miles is 29, and the standard deviation is 3.6, we can use the formula for z-score:
z = (x - μ) / σ
Plugging in the values, we can solve for x:
1.5 = (x - 29) / 3.6
Multiplying both sides by 3.6, we get:
1.5 * 3.6 = x - 29
5.4 = x - 29
x = 5.4 + 29
x ≈ 34.4
So, the closest mileage within a z-score of 1.5 would be 36 miles.
But hey, don't fret! You've got some wiggle room for a little detour on your daily commute!
To find which mileage is within a z-score of 1.5, we need to use the formula:
z = (x - μ) / σ
Where:
z = z-score
x = value we want to find
μ = mean number of miles
σ = standard deviation
We are given:
x̄ (x-bar) = 29 (mean number of miles)
s = 3.6 (standard deviation)
To find the value within a z-score of 1.5, we first need to calculate the z-value corresponding to 1.5. We can do this using the formula:
z = (x - x̄) / s
Substituting the given values:
1.5 = (x - 29) / 3.6
Next, we can solve for x by multiplying both sides of the equation by 3.6 and rearranging:
1.5 * 3.6 = x - 29
5.4 = x - 29
Adding 29 to both sides:
5.4 + 29 = x
34.4 = x
Therefore, the mileage within a z-score of 1.5 is 34.4 miles. None of the given options (21 miles, 24 miles, 36 miles, 41 miles) match this result.