Statistics and Probability Answers

(3.3.17) Use the following cell phone airport data speeds​ (Mbps) from a particular network. Find the percentile corresponding to the data speed 9.3 Mbps.
0.2, 0.3, 0.3, 0.3, 0.3, 0.4, 0.4, 0.5, 0.5, 0.6
0.6, 0.6, 0.7, 0.8, 0.9, 0.9, 1.2, 1.3, 1.4, 1.7
1.7, 1.9, 2.2, 2.2, 2.4, 2.6, 2.8, 3.4, 3.5, 4.2
4.2, 4.4, 5.9, 6.2, 6.6, 6.6, 7.5, 9.3, 10.2, 10.3
10.9, 11.7, 12.1, 13.2, 13.3, 13.8, 14.5, 14.7, 15.6, 30.8
Percentile of 9.3=

(3.3.16) In a recent awards​ ceremony, the age of the winner for best actor was 32 and the age of the winner for best actress was 50. For all best​ actors, the mean age is 41.3 years and the standard deviation is 5.4 years. For all best​ actresses, the mean age is 35.3 years and the standard deviation is 10.2 years.​ (All ages are determined at the time of the awards​ ceremony.) Relative to their​ genders, who had the more extreme age when winning the​ award, the actor or the​ actress? Explain.

Since the z score for the actor is z= ,and the z score for the actress is z=,the actress/actor had the more extreme age.

(3.3.15) Based on sample​ data, newborn males have weights with a mean of 3243.4g and a standard deviation of 574.9g. Newborn females have weights with a mean of 3025.6g and a standard deviation of 724.6g. Who has the weight that is more extreme relative to the group from which they​ came: a male who weighs 1700g or a female who weighs 1700​g?'

Since the z score for the male is z= and the z score for the female is z=, the male/female has the weight that is more extreme

(3.3.13) The tallest living man at one time had a height of 244 cm. The shortest living man at that time had a height of 65.5 cm. Heights of men at that time had a mean of 172.29 cm and a standard deviation of 7.64 cm. Which of these two men had the height that was more​ extreme?

Since the z score for the tallest man is z= and the z score for the shortest man is z=
​, the tallest/shortest man had the height that was more extreme (Round to two decimals)

(3.3.11) Consider a value to be significantly low if its z score less than or equal to -2 or consider a value to be significantly high if its z score is greater than or equal to 2.
A data set lists weights​ (grams) of a type of coin. Those weights have a mean of 5.28353 g and a standard deviation of 0.06149 g. Identify the weights that are significantly low or significantly high.
What weights are significantly​ low?
A.Weights that are less than

B.Weights that are between and
.
C.Weights that are greater than

(3.3.9) Consider a value to be significantly low if its z score less than or equal to -2 or consider a value to be significantly high if its z score is greater than or equal to 2.
A test is used to assess readiness for college. In a recent​ year, the mean test score was 20.5 and the standard deviation was 4.9. Identify the test scores that are significantly low or significantly high.

What test scores are significantly​ low?
Test scores that are between and

(3.3.8) A data set lists weights​ (lb) of plastic discarded by households. The highest weight is 5.64 ​lb, the mean of all of the weights is x=2.112 ​lb, and the standard deviation of the weights is s=1.111 lb.
a. What is the difference between the weight of 5.64 lb and the mean of the​ weights?
b. How many standard deviations is that​ [the difference found in part​ (a)]?
c. Convert the weight of 5.64 lb to a z score.
d. If we consider weights that convert to z scores between -2 and 2 to be neither significantly low nor significantly​ high, is the weight of 5.64 lb​ significant?

(3.3.7) For a data set of the pulse rates for a sample of adult​ females, the lowest pulse rate is 34 beats per​ minute, the mean of the listed pulse rates is x=74.0 beats per​ minute, and their standard deviation is s=15.8 beats per minute.
a. What is the difference between the pulse rate of 34 beats per minute and the mean pulse rate of the​ females?
b. How many standard deviations is that​ [the difference found in part​ (a)]?
c. Convert the pulse rate of 34 beats per minutes to a z score.
d. If we consider pulse rates that convert to z scores between 2 and 2 to be neither significantly low nor significantly​ high, is the pulse rate of beats per minute​ significant?

(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?

(3.2.42) The body temperatures of a group of healthy adults have a​ bell-shaped distribution with a mean of 98.11F and a standard deviation of 0.56F. Using the empirical​ rule, find each approximate percentage below. ( for A do not round)
a. What is the approximate percentage of healthy adults with body temperatures within 1 standard deviation of the​ mean, or between 97.55F and 98.67​F?
b. What is the approximate percentage of healthy adults with body temperatures between 96.43F and 99.79F