SOLUTION: CNNBC recently reported that the mean annual cost of auto insurance is 1016 dollars. Assume the standard deviation is 268 dollars. You take a simple random sample of 61 auto insura

Question 1133709: CNNBC recently reported that the mean annual cost of auto insurance is 1016 dollars. Assume the standard deviation is 268 dollars. You take a simple random sample of 61 auto insurance policies.
1. Find the probability that a single randomly selected value is less than 990 dollars.
P(X < 990) = ____________(Enter your answers as numbers accurate to 4 decimal places)

2. Find the probability that a sample of size
n= 61 is randomly selected with a mean less than 990 dollars.
P(M < 990) = __________(Enter your answer as numbers accurate to 4 decimal places)
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
1. z<=(x-mean)/sd or <=(990-1016)/268 or -26/268 or -0.10. Assume the sd is known as a population since the sample sd is not given.
probability z is less than that is 0.4602
2. z<=(x-mean)/sigma/sqrt(n), assuming the sd is known as a population.
z<=(990-1016)/268/sqrt(61)
z<=(-26*sqrt(61))/268 or -0.76. I use z to two decimal places
that probability is 0.2236
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