1)z Scores LeBron James, one of the most successful basketball players of all time, has a height of 6 feet 8 inches, or 203 cm. Based on statistics from Data Set 1 "Body Data" in Appendix B, his height converts to the z score of 4.07. How many standard deviations is his height above the mean?

2)Boxplot Comparison Refer to the boxplots shown below that are drawn on the same scale. One boxplot represents the weights of men, and the other boxplot represents the weights of women. Which boxplot represents the weights of women? Explain.

3) ATL Data Speeds For the Verizon airport data speeds (Mbps) listed in Data Set 32 "Airport Data Speeds" in Appendix B, the highest speed of 77.8 Mbps was measured at Atlanta's (ATL) international airport. The complete list of 50 Verizon data speeds has a mean of x = 17.60 Mbps and a standard deviation of s = 16.02 Mbps.

.a. What is the difference between Verizon's data speed at Atlanta's international airport and the mean of all of Verizon's data speeds?

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

c. Convert Verizon's data speed at Atlanta's international airport 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 Verizon's speed at Atlanta significant?

 

4.Female Pulse Rates of adult females are listed in Data Set 1 "Body Data" in Appendix B. The lowest pulse rate is 36 beats per minute, the mean of the listed pulse rates is x = 74.0 beats per minute, and their standard deviation is s = 12.5 beats per minute.

 

a. What is the difference between the pulse rate of 36 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 36 beats per minute 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 36 beats per minute significant?

1. The z score measures the number of standard deviation that the value is from the mean.

Thus,

- If the z-score is positive (z > 0), then the value is above the mean.

- If the z-score is negative (z < 0), then the value is below the mean.

Suppose a player has a height of 203 cm (6 feet and 8 inches)

The height of 203 cm converts to the z score of 4.07.

Here, the z score is 4.07, which is positive. It means that the height of 203 cm is 4.07 standard deviations above the mean.

2. Box plot shows the five number summary of the data. Starting from the left most number the first number sows the minimum value, second number shows first quartile, third number shows median, fourth number shows the third quartile, and fifth number shows the maximum value. In general, men have greater height and weight than women. First box shows the median of data is 84.4 and second box plot shows median is 74. And minimum value of first box plot is 50.3 and for second box plot is 39. That is second box plot shows data have less weight. So, it seems that the second box plot show the weight of women.

3.

a. Let x? shows the mean and s shows the sample standard deviation. The formula for z score is: z= sx−x??. That is z-score shows that number of standard deviation the score is above or below the mean. The higher the z score shows that more number of scores less than his z-scores.

Given:

x?=17.60mbps,s=16.02mbps

The speed of Atlanta's international airport is x = 77.8. So the required difference will be:

x−x?=77.8−17.60=60.2

Hence, difference between Verizon's data speed at Atlanta's international airport and the mean of all of Verizon's data speeds is 60.2 mbps.

b. The number of standard deviation the difference is equal to z score. The z score for difference will be:

z= sx−x??

= 60.2 / 16.02

= 3.76

Hence, difference is 3.76 standard deviations.

c. The z score will be

z= sx−x??

= 60.2 / 16.02

= 3.76

The z score of speed at Atlanta is greater than 2 so it means that it is significantly high. Thus, Verizon's speed at Atlanta is significant.

4. 

a. Let x? shows the mean and s shows the sample standard deviation. The formula for z score is: z= sx−x??. That is z-score shows that number of standard deviation the score is above or below the mean. The higher the z score shows that more number of scores less than his z-scores.

Given:

x?=74bpm,s=12.5bpm

The required difference between x = 36 will be:

x−x?=36−74=−38

Hence, the difference between the pulse rates is -38 minutes per minutes.

b.  The number of standard deviation the difference is equal to z score. The z score for difference will be:

z= sx−x??

= -38 / 12.5

= -3.04

Hence, difference is -3.04 standard deviations below.

c. The z score will be:

z= sx−x??

= -38 / 12.5

= -3.04

Hence, difference is -3.04 standard deviations below.

d. The z score of 36 beats pr minute is less than -2, so it significantly low. Hence, the pulse rate of 36 beats per minute is significant.