At the end of the spring semester, the dean of students sent a survey to the entire freshman class. One question asked the students how much weight they had gained or lost since the beginning of the school year. The average was a gain of u = 9 pounds with a standard deviation of o = 6. The distribution of scores was approximately normal. A sample of n = 4 students is selected, and the average weight change is computed for the sample. What is the probability that the sample mean will be a gain of between M = 9 and M = 12 pounds? In symbols, what is p(9 < M < 12)? (four decimals)

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At the end of the spring semester, the dean of students sent a
survey to the entire freshman class. One question asked the
students how much weight they had gained or lost since the
beginning of the school year.
The average was a gain of u = 9 pounds with a standard deviation
of o = 6. The distribution of scores was approximately normal.
A sample of n = 4 students is selected, and the average weight
change is computed for the sample.
What is the probability that the sample mean will be a gain of
between M = 9 and M = 12 pounds? In symbols, what is p(9 < M <
12)? (four decimals)
Transcribed Image Text:At the end of the spring semester, the dean of students sent a survey to the entire freshman class. One question asked the students how much weight they had gained or lost since the beginning of the school year. The average was a gain of u = 9 pounds with a standard deviation of o = 6. The distribution of scores was approximately normal. A sample of n = 4 students is selected, and the average weight change is computed for the sample. What is the probability that the sample mean will be a gain of between M = 9 and M = 12 pounds? In symbols, what is p(9 < M < 12)? (four decimals)
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