Mathematics, 07.06.2020 02:00 burnsmykala23

Recently, FHA mortgages, which are insured by the federal government, accounted for 28% of all home-purchase mortgages that were approved. A random sample of 150 mortgage applications was selected. What is the probability that 48 or more from this sample were insured by the FHA?

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Answer from: quavion61

15.87% probability that 48 or more from this sample were insured by the FHA

Step-by-step explanation:

I am going to use the normal approximation to the binomial to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

p = 0.28, n = 150

$\mu = E(X) = np = 150*0.28 = 42$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{150*0.28*0.72} = 5.5$

What is the probability that 48 or more from this sample were insured by the FHA?

Using continuity correction, this is $P(X \geq 48 - 0.5) = P(X \geq 47.5)$ , which is 1 subtracted by the pvalue of Z when X = 47.5. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{47.5 - 42}{5.5}$

Z = 1

Z = 1 has a pvalue of 0.8413.

1 - 0.8413 = 0.1587

15.87% probability that 48 or more from this sample were insured by the FHA

Answer from: Quest

answer: the 4 kilogram bag

step-by-step explanation: this is because if you divide the number of kilograms into the total it will tell you how much each individual kilogram would be worth. 2 kilos is 7 and change 3 would be around 6 ish and the 4 kilo would be 4.6 and change and the 5 kilos would be like 4.88

Answer from: Quest

29 mil

step-by-step explanation:

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