(20 pts) The weight of 5 year old boys is normally distributed with a mean value 110 cm and standard deviation 5 cm. a. What is the probability that a randomly chosen boy is shorter than 102 cm? b. What is the 99th percentile? c. If a random sample of 10 boys is selected and their mean weight is calculated i. What are E() and σ₂? ii. What is the probability the average height exceeds 112 cm?

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(20 pts) The weight of 5 year old boys is normally distributed with a mean value 110 cm and
standard deviation 5 cm.
a. What is the probability that a randomly chosen boy is shorter than 102 cm?
b. What is the 99th percentile?
c. If a random sample of 10 boys is selected and their mean weight is calculated
i. What are E() and σ₂?
ii. What is the probability the average height exceeds 112 cm?
Transcribed Image Text:(20 pts) The weight of 5 year old boys is normally distributed with a mean value 110 cm and standard deviation 5 cm. a. What is the probability that a randomly chosen boy is shorter than 102 cm? b. What is the 99th percentile? c. If a random sample of 10 boys is selected and their mean weight is calculated i. What are E() and σ₂? ii. What is the probability the average height exceeds 112 cm?
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