Answer to Question #143900 in Statistics and Probability for Vladimyr Lubin

Question

(3.3.5) Researchers measured the data speeds for a particular smartphone carrier at 50 airports. The highest speed measured was 72.6 Mbps. The complete list of 50 data speeds has a mean of x=16.38 Mbps and a standard deviation of s=29.86 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

a.

The difference between the highest data speed and mean is 72.6-16.38=56.22 Mps

b.

56.22 is $\frac{56.22}{29.86}=1.8828$ standard deviations.

c.

z score is equivalent to the number of standard deviations a value is from the mean. Thus, z=1.88 from part b above.

d.

The highest speed is within -2 and 2 standard deviations. Thus, it is not significantly high.