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Answer:
Probability that the average length of a sheet is between 30.25 and 30.35 inches long is 0.0214 .
Step-by-step explanation:
We are given that the population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.2 inches.
Also, a sample of four metal sheets is randomly selected from a batch.
Let X bar = Average length of a sheet
The z score probability distribution for average length is given by;
Z = ~ N(0,1)
where, = population mean = 30.05 inches
= standard deviation = 0.2 inches
n = sample of sheets = 4
So, Probability that average length of a sheet is between 30.25 and 30.35 inches long is given by = P(30.25 inches < X bar < 30.35 inches)
P(30.25 inches < X bar < 30.35 inches) = P(X bar < 30.35) - P(X bar <= 30.25)
P(X bar < 30.35) = P( <
) = P(Z < 3) = 0.99865
P(X bar <= 30.25) = P( <=
) = P(Z <= 2) = 0.97725
Therefore, P(30.25 inches < X bar < 30.35 inches) = 0.99865 - 0.97725
= 0.0214
Answer:
5.70%
Step-by-step explanation:
Correct word <em>"We turned a $25,000 investment of money in 1982 into $100,000 in 2007." What return (interest rate) did they really earn on their investment?</em>
No of years(1982 to 2007) = 25 years
The average annual return is R%, so $25,000 * (1 + R)^25 = $100,000
(1 + R)^25 = $100,000 / $25,000
(1 + R)^25 = 4
<em>We take 25th root on each side</em>
(1 + R)^(25*1/25) =
1 + R = 1.0570
R = 1.0570 - 1
R = 0.057
R = 5.70%
So, the return (interest rate) they really earn on their investment is 5.70%.