A loan company knows that 5% of its loans will be delinquent. Of the company’s 400 loan accounts, what is the probability
1 answer:
Answer:
Step-by-step explanation:
Given that a loan company knows that 5% of its loans will be delinquent.
since each loan is independent of the other p , probability for any random loan to be delinquent is constant 0.05
X no of delinquent loan accounts is binomial with n =400 and p = 0.05
Since n is very large and also np = 20 and nq >5 we can approximate to normal
Mean = np = 20 : Variance = npq = 19
Std dev = 4.36
X is N(1, 4.36)
With continuity correcton we calculate the prob
a) that exactly 25 accounts will be delinquent?
=
b) that fewer than 30 accounts will be delinquent?
=P(X<29.5)
= 0.9854
c) more than 24 accounts will be delinquent
=P(X>24,5)
=0.1509
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9514 1404 393
Answer:
(b) 15.32
Step-by-step explanation:
You can use your triangle sense to answer this.
The side x will always be shorter than the hypotenuse, 20. This eliminates the last two choices.
If the angle is 45°, then the sides are equal at about 0.707 times the length of the hypotenuse. That would make them 0.707×20 = 14.14. Since the angle is greater than 45°, the opposite side will be greater than 14.14. Only one answer choice fits between 14 and 20: the second choice -- 15.32.
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The mnemonic SOH CAH TOA reminds you of the relation ...
Sin = Opposite/Hypotenuse
sin(50°) = x/20
x = 20×sin(50°) . . . . multiply by 20 to find x
x ≈ 15.32 . . . . . . . . . use your calculator to evaluate
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The attachment is intended to show how the triangle side lengths change with angle.
