Question

Researchers measured the data speeds for a particular smartphone carrier at 50 airports. The highest speed measured was 71.3 Mbps. The complete list of 50 data speeds has a mean of x=18.29 Mbps and a standard deviation of s=20.59 Mbps.

a. What is the difference between​ carrier's highest data speed and the mean of all 50 data​ speeds?

b. How many standard deviations is that​ [the difference found in part​ (a)]?

c. Convert the​ carrier's highest data speed to a z score.

d. If we consider data speeds that convert to z scores between -2 and 2 to be neither significantly low nor significantly​ high, is the​ carrier's highest data speed​ significant?

Answer 1

Kindly check explanation

Explanation:

Given the following :

Highest speed measured = 71.3 Mbps

Mean speed (x) = 18.29 Mbps

Standard deviation (s) = 20.59

a.) What is the difference between​ carrier's highest data speed and the mean of all 50 data​ speeds?

(71.3 - 18.29) Mbps = 53.01 Mbps

b. How many standard deviations is that​ [the difference found in part​ (a)]?

53.01 / 20.59 = 2.57

c. Convert the​ carrier's highest data speed to a z score.

Zscore = (score - mean) / standard deviation

Zscore = (71.3 - 18.29) / 20.59

Zscore = 2.57

d. If we consider data speeds that convert to z scores between -2 and 2 to be neither significantly low nor significantly​ high, is the​ carrier's highest data speed​ significant?

Yes, this highest speed is significant as it's Zscore is higher than 2 (2.57).