1.9 HW
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 54. For all best actors, the mean age is 42.8 years and the standard deviation is 7.2 years. For all best actresses, the mean age is 38.5 years and the standard deviation is 11.1 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= -1.5 and the z score for the actress is z= 1.40, the actor has the more extreme age.
Based on sample data, newborn males have weights with a mean of 3203.6 g and a standard deviation of 797.6 g. Newborn females have weights with a mean of 3011.2 g and a standard deviation of 520.6 g. Who has the weight that is more extreme relative to the group from which they came: a male who weighs 1700 g or a female who weighs 1700 g?
Since the z score for the male is z = -1.89 and the score for the female is z = -2.52, the female has the weight that is more extreme.
The tallest living man at one time had a height of 248 cm. The shortest living man at that time had a height of 55.1 cm. Heights of men at that time had a mean of 175.31 cm and a standard deviation of 7.48 cm. Which of these two men had the height that was more extreme?
Since the z score for the tallest an is z = 9.72 and the z score for the shortest man is z = -16.07, the shortest man had the height that was more extreme.
Find the percentile corresponding to 0.85 W/kg
The percentile corresponding to 0.85 W/kg is 18.
Find the percentile corresponding to 1.51 W/kg
The percentile corresponding to 1.51 is W/kg is 94
A successful basketball player has a height of 6 feet 2 inches, or 188 cm. Based on statistics from a data set, his height converts to the z score of 1.95. How many standard deviations is his height above the mean?
The player's height is 1.95 standard deviation(s) above the mean.
If your score on your next statistics test is converted to a z score, which of these z scores would you prefer: −2.00, −1.00, 0, 1.00, 2.00? Why?
The z score of 2.00 is most preferable because it is 2.00 standard deviations above the mean and would correspond to the highest of the five different possible test scores.
A test is used to assess readiness for college. In a recent year, the mean test score was 22.6 and the standard deviation was 4.9. Identify the test scores that are significantly low or significantly high.
What are scores that are significantly low? Test scores that are less than 12.8 What test scores are significantly high? Test scores that are greater than 32.4
In designing a work desk, it is found that males have sitting knee heights with a mean of 22.2 in. and a standard deviation of 1.5 in. (based on data from the Department of Transportation). Use the range rule of thumb to identify (a) the values that are significantly low, (b) the values that are significantly high, and (c) the values that are neither significantly low nor significantly high.
What heights are significantly low? Heights that are less than 19.2 in What heights are significantly high? Heights that are greater than 25.2 in What heights are neither significantly low nor significantly high? Heights that are greater than 19.2 in and less than 25.2 in
For a data set of the pulse rates for a sample of adult females, the lowest pulse rate is 33 beats per minute, the mean of the listed pulse rates is x=75.0 beats per minute, and their standard deviation is s=13.1 beats per minute. a. What is the difference between the pulse rate of 33 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 33 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 33 beats per minute significant?
a. The difference is 42 beats per minute b. The difference is 3.21 standard deviations c. The z score is z= -3.21 d. The lowest pulse rate is significantly low
Researchers measured the data speeds for a particular smartphone carrier at 50 airports. The highest speed measured was 72.2 Mbps. The complete list of 50 data speeds has a mean of x=15.79 Mbps and a standard deviation of s=31.27 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?
a. The difference is 56.41 Mbps b. The difference is 1.80 standard deviations c. The z score is z= 1.80 d. The carrier's highest data speed is not significant
