SOLUTION: If a random sample of eight 18-year-old men is selected, what is the probability that the mean height x is between 70 and 72 inches? (Round your answer to four decimal places.)
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Question 1172750: If a random sample of eight 18-year-old men is selected, what is the probability that the mean height x is between 70 and 72 inches? (Round your answer to four decimal places.)
Suppose the heights of 18-year-old men are approximately normally distributed, with mean 71 inches and standard deviation 1 inches.
You can put this solution on YOUR website! Probability the mean height is less than 72 inches:
z1 = = 2.83
A z-score of 2.83 is 0.9977. This means there is a 0.9977 probability the mean height will be below 72 inches.
Probability the mean height is less than 70 inches:
z2 = = -2.83
A z-score of -2.83 is 0.0023. This means there is a 0.0023 probability the mean height will be below 70 inches.
To find the probability the mean height will be between 70 and 72 inches, simply subtract these two probabilities from one another:
0.9977 - 0.0023 = 0.9954 There is a 0.9954 probability the mean height will be between 70 and 72 inches.
