Answer:
a: 0.8884
b: 0.9934
Step-by-step explanation:
We have µ = 300 and σ = 70. The sample size, n = 125.
For the sample to be within 8 units of the population mean, we would have sample values of 292 and 308, so we want to find:
P(292 < x < 308).
We need to find the z-scores that correspond to these values using the given data. See attached photo 1 for the calculation of these scores.
We have P(292 < x < 308) = 0.8884
Next we want the probability of the sample mean to be within 17 units of the population mean, so we want the values from 283 to 317. We want to find
P(283 < x < 317)
We need to find the z-scores that correspond to these values. See photo 2 for the calculation of these scores.
We have P(283 < x < 317) = 0.9934
The location of point Y is the point -3 on the number line
Here, we want to find the location of Y
let us say the point 0 represents the origin
The coordinates of point x will be (-9,0) while the coordinates of point z will be (3,0)
To find the location of Y , we proceed to use the midpoint formula as follows;
Thus, we have;
(-9 + 3)/2 , (0 + 0)/2
= -6/2 , 0
= (-3 , 0)