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ludmilkaskok [199]
3 years ago
15

According to a recent survey, 31 percent of the residents of a certain state who are age 25 years or older have a bachelor’s deg

ree. A random sample of 50 residents of the state, age 25 years or older, will be selected. Let the random variable B represent the number in the sample who have a bachelor’s degree. What is the probability that B will equal 40 ?
Mathematics
2 answers:
lesya692 [45]3 years ago
5 0

Answer:

(50 (0.31)^40(0.69)^10

40

Inga [223]3 years ago
4 0

Answer:

The probability of  getting B=40 is 0.11\times 10^{-11} which is negligible.

Step-by-step explanation:

Given that 31 percent of the residents of a certain state who are age 25 years or older have a bachelor’s degree.

Assuming the population of the state aged 25 years or more is Bernoulli's population.

So, when 1 person aged 25 years or more from the state selected randomly, the probability of that person, p, having a bachelor’s degree,

p= 31/100=0.31\cdots(i)

Now, according to Bernoulli's formula, the probability of exactly r success from the total number of sample n is

P(r)=\binom{n} {r}p^r(1-p)^{n-r}\cdots(ii)

where p is the probability of success.

Here, a random sample of 50 residents of the state, age 25 years or older, will be selected.

So, n=50.

Given that variable B represents the number in the sample who have a bachelor’s degree,

We have to find the probability that B will equal 40.

So, r=B= 40.

Now, putting these values in equation(ii) and using p=0.25 from equation (i), we have

P(r=40)=\binom{50} {40}(0.31)^{40}(1-0.31)^{50-40}

=\frac {50!}{40! (50-40)!}(0.31)^{40}(0.69)^{10} \\\\=\frac {50!}{40! \times 10!}(0.31)^{40}(0.69)^{10} \\\\=0.11\times 10^{-11}

So, the probability of  getting B=40 is 0.11\times 10^{-11} which is negligible.

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