Question

In: Statistics and Probability

Fifty percent of households say they would feel secure if they had​ $50,000 in savings. You...

Fifty percent of households say they would feel secure if they had​ $50,000 in savings. You randomly select 8 households and ask them if they would feel secure if they had​ $50,000 in savings. Find the probability that the number that say they would feel secure is​ (a) exactly​ five, (b) more than​ five, and​ (c) at most five.

​(a) Find the probability that the number that say they would feel secure is exactly five.

​P(5)=_ ​(Round to three decimal places as​ needed.)

​(b) Find the probability that the number that say they would feel secure is more than five.

​P(x>​5)=_ (Round to three decimal places as​ needed.)

​(c) Find the probability that the number that say they would feel secure is at most five.

​P(x≤​5)=_ (Round to three decimal places as​ needed.)

Solutions

Expert Solution

a)

It is given that

X is random variable for number of household that will feel secure if thet had $50000 for saving

Probability P=0.5 will be success of probability (proportion of household that feel secure if they had $50000 in savings

Probability of failure will be also =0.5=Q=1-P

N=8 number of independent trails

Using the binomial distribution formula

We have to find the e probability that the number that say they would feel secure is exactly five.

b)

We have to Find the probability that the number that say they would feel secure is more than five.​P(x>​5)

Let us first solve the part c

c)

Find the probability that the number that say they would feel secure is at most five.​P(x≤​5)

Let us find the probability

Now we will find the part b

b)

We have to Find the probability that the number that say they would feel secure is more than five.​P(x>​5)

orchestra answered 2 years ago
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