In a certain large city, 45% of families earn less than $35,000 per year. Assuming the distribution is binomial and you can use the exact binomial calculation, what's the probability, accurate to the number of decimal places given, that a simple random sample of 30 families will have 10 or fewer families earning less than $35,000 per year? Use the exact binomial calculation.

Question

In a certain large city, 45% of families earn less than $35,000 per year. Assuming the distribution is binomial and you can use the exact binomial calculation, what's the probability, accurate to the number of decimal places given, that a simple random sample of 30 families will have 10 or fewer families earning less than $35,000 per year? Use the exact binomial calculation.

Α. 0656373968

Β. 0990882214

C. .1350263968

D. .1350447033

Ε. .0694073054

Answer 1

To calculate this probability, we can use the binomial probability formula:

P(X ≤ 10) = Σ (from k = 0 to 10) [(30 choose k) * (0.45^k) * (0.55^(30-k))]

Calculating this gives us:

P(X ≤ 10) = [ (30 choose 0) * (0.45^0) * (0.55^30) ] + [ (30 choose 1) * (0.45^1) * (0.55^29) ] + ... + [ (30 choose 10) * (0.45^10) * (0.55^20) ]

The result is approximately 0.1350447033, which rounded to 10 decimal places is 0.1350447033, making the correct answer choice:

D. .1350447033