A: You recently took a statistics class in a large class with n = 500 students....

A: You recently took a statistics class in a large class with n = 500 students. The instructor tells the class that the scores were Normally distributed, with a mean of 7 2 (out of 100 ) and a standard deviation of 8 , but when you talk to other students in the class, you find out that more than 30 students have scores below 45 . That violates which rule for the Normal distribution?

the 30–60–90 rule

the 1–2–3 rule

the 68–95–99.7 rule

It does not violate any rule; anything can happen.

B: In a population of Siberian flying squirrels in western Finland, assume that the the number of pups born to each female over her lifetime has mean ?=3.66μand standard deviation ?=2.9598. The distribution of squirrel pups born is non‑normal because it takes only whole, non‑negative values.

Determine the mean number of pups, x¯, such that in 90%of all random samples of such squirrels of size ?=60,, the mean number of pups born to females in the sample is less than ?⎯⎯⎯.than x¯.

You may need to use software or a table of ?-critical values. You may find some software manuals useful.

Give your answer to at least two decimal places.

Solutions

Expert Solution

For Question A. It violates the 68-95-99.7 rule as score less than 45 does not lie in the range of either of the 68%,95% or 99.7% students.

For Question B, we use the formula mentioned and the z value from the p value is attached from STATKEY (image attached for reference).

orchestra answered 1 year ago

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