Solve for c ) if you could help I would appreciate
2 answers:
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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
Answer:
a) Effective annual rate: 18.6%
b) Effective annual rate: 20.27%
c) Effective annual rate: 20.43%
d) Effective annual rate: 20.44%
Step-by-step explanation:
The effective annual interest rate, if it is not compounded continuously, is given by the formula
where
<em>C = Amount of the credit granted </em>
<em>r = nominal interest per year </em>
<em>n = compounding frequency </em>
<em>t = the length of time the interest is applied. In this case, 1 year. </em>
In the special case the interest rate is compounded continuously, the interest is given by
(a) Annually
The effective annual rate is 18.6%
(b) Monthly
<em>There are 12 months in a year </em>
The effective annual rate is 20.27%
(c) Daily
<em>There are 365 days in a year </em>
The effective annual rate is 20.43%
(d) Continuously
The effective annual rate is 20.44%
Check the picture below.
