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What is the probability that all four will hold between 14.75 and 15.10 gallons of gas?
If a simple random sample of four tanks is selected, and their capacities can be considered independent, what is the probability that all four will hold between 14.75 and 15.10 gallons of gas?
A) 0.2397
B)0.6808
C)0.9084
D)2.7988
Approximately normal distribution with a mean of 15 gallons and a standard deviation of .15 gallons.
Please explain how you got your answer.
1 Answer
- ATumorNamedMarlaLv 41 decade agoFavorite Answer
Let c be the capacity of a gas tank.
Then if you standardize your variable:
P(c < 15.10) = P( z < (15.10 - 15) / 0.15 )
= P ( z < 0.10/0.15)
= P (z < 2/3)
On a z-table, the number the comes up for this is:
0.7475
And P(c < 14.75) = P(z < (14.75 - 15)/0.15 )
= P(z < - 5/3)
On the table, this is:
0.0478
What we want, though, is
P( 14.75 < c < 15.10)
= P(-5/3 < z < 2/3)
= P(z - 2/3) - P (z < -5/3) = 0.7475 - 0.0478 = 0.6997
This is the probability that any one gas tank will fall in the given range.
They're independent events, so the probability that four randomly selected tanks are in thsi range is
(0.6997)^4 = 0.2397 or about 24%
