Comment briefly on the following statements : (i) A computer obtained the standard deviation of 20 observations whose values ranged from 65 to 85 as 25. (ii) A student obtained the mean and variance of a set of 10 observations as 10, – 5 respectively. (iii) The range is the perfect mea m&tA¨variability as it includes all the measurements. (iv) For the distr:bution of 5 obsem Bns : 8, 8, 8, 8, 8; mean = 8 and variance = 8. (v) If the mean and s.d. of distribution A are smaller than the mean and s.d. of distribution B respectively, then the distribution A is more uniform (less variable) than the distribution B.

Use z scores to compare the given values. The tallest living man at one time had a height of 238 cm. The shortest living man at that time had a height of 142.4 cm. Heights of men at that time had a mean of 175.45 cm and a standard deviation of 5.59 cm. Which of these two men had the height that was more extreme? ... Since the z score for the tallest man is z = 0 and the z score for the shortest man is z = the man had the height that was Im- more extreme. (Round to two decimal places.) shortest tallest

For a data set of the pulse rates for a sample of adult​ females, the lowest pulse rate is 38 beats per​ minute, the mean of the listed pulse rates is x=79.0 beats per​ minute, and their standard deviation is s=22.1 beats per minute.   a. What is the difference between the pulse rate of 38 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 38 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 38 beats per minute​ significant?

7.

A rugby team from the country of Atlantis is formed by randomly drawing from its population. The population distribution is normally distributed with a mean of 165 cm and a standard deviation of 10 cm. The team draws 26 people for the team. Given a population mean of 165cm, how many standard deviations would a sample mean of 163cm be from the true value? Give your answer rounded to two decimal places.

The results from a statistics class’ first test are as follows: The average grade obtained on the test by its 45 students is an 85, with a standard deviation of 15 points. Answer the following based on this information: a. Approximately how many people received a failing grade (less than 65) b. What percentage of people received a grade between a 70 and a 91? c. What percentage of individuals received a score whose z-score was -.70 or less? d. What grade is required in order to be in the top 15 percent? The top 10 percent? e. What percentage of people received a grade between 85 and 95? f. What percentage of people received a grade of 94 or less? g. What grade is required to be in the bottom 20%? h. What z-score is required to be in the top 40%? i. What percentage of individuals have a z-score between -1 and 1.40? j. What percentage of individuals have a z-score between 1.05 and 1.40?