Question

In: Statistics and Probability

In the following problem, check that it is appropriate to use the normal approximation to the...

In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities.

It is estimated that 3.8% of the general population will live past their 90th birthday. In a graduating class of 721 high school seniors, find the following probabilities. (Round your answers to four decimal places.)

(a) 15 or more will live beyond their 90th birthday


(b) 30 or more will live beyond their 90th birthday


(c) between 25 and 35 will live beyond their 90th birthday


(d) more than 40 will live beyond their 90th birthday

Solutions

Expert Solution

Solution:

It is appropriate to use the normal approximation to the binomial because the sample size is very large(721).
Mean μ = np = 721*0.038 = 27.39800
Standard deviation σ = sqrt(np(1-p)) = sqrt(721*0.038 (1-0.038)) = 5.13
a) 15 or more will livw beyond their 90th birthday
P(x ≥ 15) = P(z ≥ 15 - 27.39/5.13)
= P(Z ≥ -2.4152)
= 0.9921 => Use the excel formula = "1- NORMSDIST(-2.4152)"

b) 30 or more will live beyond their 90th birthday
P(x ≥ 30) = P(z ≥ 30 - 27.39/5.13)
= P(Z ≥ 0.5087)
= 0.3054 => Use the excel formula = "1- NORMSDIST(0.5087)"
c) between 25 and 35 will live beyond their 90th birthday
P(25 < x < 35) = P(25 - 27.39/5.13 < z < 35 - 27.39/5.13)
= P(-0.4658 < Z < 1.4834)
= P(z < 1.4834) - P(z < -0.4658)
= 0.0689 - 0.6793
= 0.6104  

(d) more than 40 will live beyond their 90th birthday
40 or more will live beyond their 90th birthday
P(x ≥ 40) = P(z ≥ 40 - 27.39/5.13)
= P(Z ≥ 2.4581)
= 0.0069 => Use the excel formula = "1- NORMSDIST(2.458)"


Related Solutions

In the following problem, check that it is appropriate to use the normal approximation to the...
In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. Do you try to pad an insurance claim to cover your deductible? About 43% of all U.S. adults will try to pad their insurance claims! Suppose that you are the director of an insurance adjustment office. Your office has just received 140 insurance claims to be processed in the next few days. Find...
In the following problem, check that it is appropriate to use the normal approximation to the...
In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. Do you try to pad an insurance claim to cover your deductible? About 39% of all U.S. adults will try to pad their insurance claims! Suppose that you are the director of an insurance adjustment office. Your office has just received 126 insurance claims to be processed in the next few days. Find...
In the following problem, check that it is appropriate to use the normal approximation to the...
In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. Do you try to pad an insurance claim to cover your deductible? About 40% of all U.S. adults will try to pad their insurance claims! Suppose that you are the director of an insurance adjustment office. Your office has just received 120 insurance claims to be processed in the next few days. Find...
In the following problem, check that it is appropriate to use the normal approximation to the...
In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. Do you try to pad an insurance claim to cover your deductible? About 36% of all U.S. adults will try to pad their insurance claims! Suppose that you are the director of an insurance adjustment office. Your office has just received 140 insurance claims to be processed in the next few days. Find...
In the following problem, check that it is appropriate to use the normal approximation to the...
In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. Do you try to pad an insurance claim to cover your deductible? About 36% of all U.S. adults will try to pad their insurance claims! Suppose that you are the director of an insurance adjustment office. Your office has just received 124 insurance claims to be processed in the next few days. Find...
In the following problem, check that it is appropriate to use the normal approximation to the...
In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. Do you try to pad an insurance claim to cover your deductible? About 45% of all U.S. adults will try to pad their insurance claims! Suppose that you are the director of an insurance adjustment office. Your office has just received 124 insurance claims to be processed in the next few days. Find...
In the following problem, check that it is appropriate to use the normal approximation to the...
In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. Do you try to pad an insurance claim to cover your deductible? About 40% of all U.S. adults will try to pad their insurance claims! Suppose that you are the director of an insurance adjustment office. Your office has just received 140 insurance claims to be processed in the next few days. Find...
In the following problem, check that it is appropriate to use the normal approximation to the...
In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. Ocean fishing for billfish is very popular in the Cozumel region of Mexico. In the Cozumel region about 42% of strikes (while trolling) resulted in a catch. Suppose that on a given day a fleet of fishing boats got a total of 29 strikes. Find the following probabilities. (Round your answers to four...
In the following problem, check that it is appropriate to use the normal approximation to the...
In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. Do you try to pad an insurance claim to cover your deductible? About 37% of all U.S. adults will try to pad their insurance claims! Suppose that you are the director of an insurance adjustment office. Your office has just received 138 insurance claims to be processed in the next few days. Find...
In the following problem, check that it is appropriate to use the normal approximation to the...
In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. Do you try to pad an insurance claim to cover your deductible? About 37% of all U.S. adults will try to pad their insurance claims! Suppose that you are the director of an insurance adjustment office. Your office has just received 138 insurance claims to be processed in the next few days. Find...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT