points). Consider a population of 100 basketball players having a mean and a sta
ID: 2921475 • Letter: P
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points). Consider a population of 100 basketball players having a mean and a standard deviation of 3 inches. The distribution of basketball player heights is even height of 72 inches below 20 18 16 14 12 10 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 8 Player Heights (Inches Estimate the percentage of basketball players that have a height equal to or below 66 inches based on the above histogram? How does th for which the median height equals 66 inches a) is percentage compare to the population of student heights b) Suppose that an individual with a height of 68 inches is interested in trying out for the team. If this student makes the team, would this student's height be an outlier compared to the rest of the basketball players? Base your answer on a z-score calculation.Explanation / Answer
a. The frquency of players with height less than or equal to 66 that is 64, 65 and 66 are 1, 2 and 3 respectively. Thus, the cumulative frequency is: 6. There are in total 100 basketball players. Therefore, the required percentage is: 6/100*100=6%. The median M is the midpoint of any distribution, the number such that half the observations are smaller and the half of the observations are larger. Therefore, for a population which has median height 66 inches, implies 6% of the observations are below 66 and 6% of observations are above 66.
b. Compute standard score by computing the z score.
z=(x-mu)/sigma, where, x is the raw score, mu is the population mean and sigma is the population standard deviation.
z=(68-72)/3=-1.33
Thus, the aspiring entrant has a height 1.33 standard deviations below the mean. The height is within 3 standard deviations from mean, and cannot be considered an outlier.
c. The z score for height=79 is as follows:
z=(79-72)/3=2.33
Thus, the new aspiring entrant has a height 2.33 standard deviations above the mean. The height is within 3 standard deviations from mean, and cannot be considered an outlier.
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