Suppose the heights of adult males in a population have a normal distribution with mean µ = 71 inches and standard deviation σ = 3 inches. Two unrelated men will be randomly sampled. Let X = height of the first man and Y = height of the second man.
(a) Consider D = X − Y , the difference between the heights of the two men. What type of distribution will the variable D have?
(b) What is the mean value for the distribution of D?
(c) Assuming independence between the two men, find the standard deviation of D.
(d) Determine the probability that the first man is more than 3 inches taller than the second man. That is, find P(D >
(e) Find the probability that one of the men is at least three inches taller than the other. That is, find the probability that either D > 3 or D < −3.
Suppose the heights of adult males in a population have a normal distribution with mean µ...
6. The heights of men selected from a particular population have a normal distribution with mean 68 inches and standard deviation 4 inches. a. Find the percentage of men in the population who are taller than 72 inches. b. . Find the percentage of men who are between 64 and 74 inches tall C. Suppose 25% of men in this population are taller than Ralph. How tall is Ralph?
Suppose the heights of 18-year-old men are approximately normally distributed, with mean 68 inches and standard deviation 3 inches. (a) Find the percentage of 18 year old men with height between 67 and 69 inches. (b) Find the percentage of 18 year old men taller than 6 foot. (c) if a random sample of nine 18 year old men is selected, what is the probability that their mean height is between 68 and 72 inches? (d) if a random sample...
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Adult men have heights with a mean of 69.0 inches and a standard deviation of 2.8 inches. Find the z-score of a man 59.9 inches tall. (to 2 decimal places)Adult men have heights with a mean of 69.0 inches and a standard deviation of 2.8 inches. Find the height of a man with a z-score of 1.8929
Suppose that population distribution of the variable ”waist size of adult American males in inches” is µ = 33 and σ = 3 and approximately. What is the probability of encountering a man with a waist size smaller than 28 inches? What is the probability of encountering a group of 5 men with a sample average of less than 32?
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The heights of adult men in America are normally distributed, with a mean of 69.5 inches and a standard deviation of 2.68 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.4 inches and a standard deviation of 2.53 inches. a) If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)? z = b) What percentage of men are SHORTER than 6 feet 3 inches?...
The heights of adult men in America are normally distributed, with a mean of 69.1 inches and a standard deviation of 2.69 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.6 inches and a standard deviation of 2.55 inches. a) If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)? b) If a woman is 5 feet 11 inches tall, what is her z-score...