Question

please show work.

2. Assume that SAT scores are normally distributed with meanu = 1060 and standard deviation o = 195. a. If one SAT score is selected at random, what is the probability that it is greater than 1500? b. If twenty SAT scores are selected at random, what is the probability that they have a mean greater than 1500?

Answer 1

2. a. Here we need to find

As distribution is normal we can convert x to z

$P(x>1500)=P(z>\frac{1500-1060}{195})=P(z>2.26)=0.0119$

ん 0

b. Here we need to find $P(\overline{x}>1500)$

As population is normal as per central limit theorem distribution of sample mean is also normal, so we can convert sample mean to z.

$P(\overline{x}>1500)=P(z>\frac{1500-1060}{\frac{195}{\sqrt{20}}})=P(z>10.09)=0$