please show work. 2. Assume that SAT scores are normally distributed with meanu = 1060 and...

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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 s

math Statistics-And-Probability

Answer 1

Answer #1

2. a. Here we need to find P(x>1500)

As distribution is normal we can convert x to z

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

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.

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

Answer 2

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