Answer:
The percentage of data of prediction between 40 and 70 is 0.4347 or about 43.57%., the percentage of prediction that would be more than 70 miles is 0.2389 or about 23.89%
Explanation:
Let us Recall that,
We can perform analysis using the z-score of certain values, only when the standard deviation and the men are. The z-score is the measure of how many standard deviations from the mean a certain value is known. by finding the percentage of values that is expected to be above or below a value is by applying the z-score
The first step is to find the z-score for each of these values. After that, we apply the Standard Normal Probabilities table to find the percentage between the values. The z-score given as follows,
z= x-ẋ/s
ẋ = the sample mean
s = the sample standard deviation
x = is the data value not given
The mean value is = 51.6571429
The standard deviation value is = 25.8012116
Then
The z score for 40 is given as
z = 40 – 51.6571429/ 25.8012116 = - 0.45
The z score for 70 is given as,
Z = 70 – 51.6571429/ 25.8012116 = -0.71
The table entry for both -0.45 and 0.71 is 0.3264, and 0.7611
Therefore,
find the percentage between 40 and 70, we subtract table entries to get 0.7611 - 0.3264 = 0.4347 or about 43.57%.
To find the percentage above 70, we subtract the table entry for 70 from 1 to get 1 - 0.7611 = 0.2389 or about 23.89%
Answer:
43.5% and 23.9%
Explanation:
The correct question is:
What percentage of data would you predict would be between 40 and 70 and what percentage would you predict would be more than 70 miles? Subtract the probabilities found through =NORM.DIST(70, mean, stdev, TRUE) and =NORM.DIST(40, mean, stdev, TRUE) for the “between” probability. To get the probability of over 70, use the same =NORM.DIST(70, mean, stdev, TRUE) and then subtract the result from 1 to get “more than”.
Mean; 51.6571429
Standard deviation: 25.8012116
Predicted percentage between 40 and 70: 43.57%
Actual percentage: 22.86
Predicted percentage more than 70 miles: 23.86%
Actual percentage: 37.14
SOLUTION:
Since the standard deviation and mean are given, we ca use the z-score to determine the probability of the percentages asked for in the question
The z-score formula is
z = (x-μ)/σ
where x is the data value we are looking for,
μ is the sample mean, and
σ is the sample standard deviation.
The data value should be between 40 and 70
So the z-score for 40=
(40−51.6571429)/25.8012116= −0.45
P-value of the -0.45 z-score (checked on the z-score table) = 0.3264
The z-score for 70 will be
(70−51.6571429)/25.8012116= 0.71
P-value of the 0.71 z-score (checked on the z-score table) = 0.7611
Therefore the percentage between 40 and 70= p-value at 70 - p-value at 40
= 0.7611 - 0.3264
= 0.4347 converted to percentage = 43.5%
To find the percentage above 70, we subtract the p-value at 70 from 1
1 - 0.7611 = 0.2389 converted to percentage = 23.9%
