SOLUTION: I'm struggling to calculate this, stats is one of my subjects (long distance learning), but do not understand it. Could you please show me how to calculate the following: A norm

Question 494801: I'm struggling to calculate this, stats is one of my subjects (long distance learning), but do not understand it. Could you please show me how to calculate the following:
A normal population has a mean of 75 and a standard deviation of 5. A sample of size 40 has been randomly selected. The probability that the sample mean is less than 74 is equal to:
1. 0.4207
2. 0.0020
3. 0.1038
4. 0.0548
5. 0.5793
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A normal population has a mean of 75 and a standard deviation of 5. A sample of size 40 has been randomly selected. The probability that the sample mean is less than 74 is equal to:
------------
t(74) = (74-75)/[5/sqrt(40)] = -1.2649
---
P(x-bar < 74) = P(t < -1.2649 when df = 39) = 0.1067
===========================
If you use the z-distribution you would get:
P(x-bar < 74) = P(z <-1.2649) = 0.1030
===========================
Cheers,
Stan H.
==================

1. 0.4207
2. 0.0020
3. 0.1038
4. 0.0548
5. 0.5793

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