30% of the library books in the fiction section are worn and need replacement. 10% of the nonfiction holdings are worn. The libr
ary’s holdings are 80% fiction and 20% non fiction. find the probability that a book chosen at random from this library is worn and needs replacement. Please help!
1 answer:
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Answer:
Domain:
Range:
Step-by-step explanation:
The domain of a function is the set of values that one can input into a function and get a valid result.
The range of a function is the set of valid outputs that one can attain when a value is substituted into a function.
Answer:
a) P(Y > 76) = 0.0122
b) i) P(both of them will be more than 76 inches tall) = 0.00015
ii) P(Y > 76) = 0.0007
Step-by-step explanation:
Given - The heights of men in a certain population follow a normal distribution with mean 69.7 inches and standard deviation 2.8 inches.
To find - (a) If a man is chosen at random from the population, find
the probability that he will be more than 76 inches tall.
(b) If two men are chosen at random from the population, find
the probability that
(i) both of them will be more than 76 inches tall;
(ii) their mean height will be more than 76 inches.
Proof -
a)
P(Y > 76) = P(Y - mean > 76 - mean)
= P( ) >
)
= P(Z > )
= P(Z > )
= P(Z > 2.25)
= 1 - P(Z ≤ 2.25)
= 0.0122
⇒P(Y > 76) = 0.0122
b)
(i)
P(both of them will be more than 76 inches tall) = (0.0122)²
= 0.00015
⇒P(both of them will be more than 76 inches tall) = 0.00015
(ii)
Given that,
Mean = 69.7,
= 1.979899,
Now,
P(Y > 76) = P(Y - mean > 76 - mean)
= P( )) >
)
= P(Z > )
= P(Z > ))
= P(Z > 3.182)
= 1 - P(Z ≤ 3.182)
= 0.0007
⇒P(Y > 76) = 0.0007