Normal distribution questions
Can someone check my answers for the first two questions, I have a feeling they're wrong. And I can't seem to get the right answer to question 2. a), I keep ending up with an 'impossible' z score.
Brain weights in a certain population of adult Swedish males are approximately normally distributed with a mean of 1400 g and a standard deviation of 100g.
1. a) For an individual chosen at random from this population calculate the probability that their brain weight is less than 1375 g or more than 1500 g.
=1-P(1375-1400/100 < Z < 1500-1400/100)
=1-P(-.25 < Z < 1)
=1-P(Z<1) - P(Z<-.25)
b) For a random sample of 10 from this population calculate the probability that the mean brain weight is less than 1375 g or more than 1500 g.
=P(1375-1400/(100/square root of 10 < X < 1500-1400/(100/square root of 10)
=P(-.79 < Z < 3.16)
=P(Z<3.16) - P(Z<-.79)
2 a) How do you expect the sample mean brain weight to be distributed for random samples of size 20 from this population?
b) In such samples, how unusual would it be to find a mean brain weight in excess of 1470 g?