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
Α. 0656373968
Β. 0990882214
C. .1350263968
D. .1350447033
Ε. .0694073054
Answers
GPT 3.5
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
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