1.)Heights of adult males in the US are approximately normally distributed with mean 70 inches (5 ft 10 in) and standard deviation 3 inches. a.)What proportion of US men are between 5 ft 7.6 in and 6 ft 0.4 in tall ( 67.6 and 72.4 inches, respectively)? (b) If a man is at the 8th percentile in height, how tall is he? 2.)Exam grades across all sections of introductory statistics at a large university are approximately normally distributed with a mean of 72 and a standard deviation of 11. Use the normal distribution to answer the following questions. a.)What percent of students scored above a 90 ? b.)What percent of students scored below a 64 ? (c) If the lowest 8% of students will be required to attend peer tutoring sessions, what grade is the cutoff for being required to attend these sessions? (d) If the highest 10% of students will be given a grade of A, what is the cutoff to get an A?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
1.)Heights of adult males in the US are approximately
a.)What proportion of US men are between 5 ft 7.6 in and 6 ft 0.4 in tall ( 67.6 and 72.4 inches, respectively)?
(b) If a man is at the 8th percentile in height, how tall is he?
2.)Exam grades across all sections of introductory statistics at a large university are approximately normally distributed with a mean of 72 and a standard deviation of 11. Use the normal distribution to answer the following questions.
a.)What percent of students scored above a 90 ?
b.)What percent of students scored below a 64 ?
(c) If the lowest 8% of students will be required to attend peer tutoring sessions, what grade is the cutoff for being required to attend these sessions?
(d) If the highest 10% of students will be given a grade of A, what is the cutoff to get an A?
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