Question

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?

Answer 1

43.5% and 23.9%

Step-by-step 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%

Answer 2

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%

Step-by-step 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%