Herondaleheir
New member
- Joined
- Apr 1, 2019
- Messages
- 11
Graduate students applying for entrance to many universities must take a Miller Analogies Test. It is known that the test scores have a mean of 75 and a variance of 16. In 1990, 100 students applied for entrance into graduate school in physics.
Find the probability that the sample mean deviates from the population mean by less than 1.
Teacher's solution:
P(|X¯ −µ| < 2) = P(−2 < X¯ −µ < 2) = P(−2/0.4 < Z < 2/0.4) = P(−5 < Z < 5) = P(Z <5) − P(Z < −5) ≈ 1 − 0 =1
It kind of formated weird so I put an image of the solution down if it's needed. I was wondering if someone could walk me through the teacher's solution cause I don't understand it? Like for example why does the teacher start with P(|X¯ −µ| < 2) if it mentions "less than 1" in the question? Where did the 2 come from?
Find the probability that the sample mean deviates from the population mean by less than 1.
Teacher's solution:
P(|X¯ −µ| < 2) = P(−2 < X¯ −µ < 2) = P(−2/0.4 < Z < 2/0.4) = P(−5 < Z < 5) = P(Z <5) − P(Z < −5) ≈ 1 − 0 =1
It kind of formated weird so I put an image of the solution down if it's needed. I was wondering if someone could walk me through the teacher's solution cause I don't understand it? Like for example why does the teacher start with P(|X¯ −µ| < 2) if it mentions "less than 1" in the question? Where did the 2 come from?
