1. The probability that an adult over the age of 80 uses a hearing aid is 0.314.

Question

1. The probability that an adult over the age of 80 uses a hearing aid is 0.314. Using the binomial distribution, find the probability that in a sample of 10 adults over the age of 80, 4 of them use a hearing aid.

2. The probability that someone will receive a tax refund is 0.70. Find the probability that: (You may use table A-1 for this problem)

a) at least 1 of 3 people will receive a tax refund

           b) exactly 4 of 8 people will receive a tax refund

           c) at least 4 of 8 people will receive a tax refund

           d) at most 4 of 8 people will receive a tax refund

3. A study by a polling firm shows that 36.4% of women have a graduate degree.

a) For a randomly selected group of 325 women, find the mean and standard deviation for the number that have a graduate.

b)Based on this survey, would it be unusual to find that 100 have a graduate degree? (Explain your answer.)

Explanation / Answer

. The probability that an adult over the age of 80 uses a hearing aid is 0.314. Using the binomial distribution, find the probability that in a sample of 10 adults over the age of 80, 4 of them use a hearing aid.

n = 10

P(x=4) = 10 C 4 0.314^4 (1-0.314)^(10-4) = 210*0.314^4 * 0.686^6 = 0.2127

2. The probability that someone will receive a tax refund is 0.70. Find the probability that: (You may use table A-1 for this problem)

a) at least 1 of 3 people will receive a tax refund

P(x>=1) = 1- P(x=0) = 1 - 3 C 0 0.7^0 0.3^3 = 0.973

b) exactly 4 of 8 people will receive a tax refund

P(x=4) = 8 C 4 0.7^4 0.3^4 = 70*0.7^4 *0.3^4 = 0.1361

c) at least 4 of 8 people will receive a tax refund

P(X>=4) = P(x=5) + P(x=6) +P(x=7)+ P(x=8)

= 8 C 5 0.7^5 0.3^3 + 8 C 6 0.7^6 0.3^2 + 8 C 7 0.7^7 0.3^1 + 8 C 8 0.7^8 0.3^0

= 0.9420

d) at most 4 of 8 people will receive a tax refund

P(x<=4) = P(x=0) + P(x=1) + P(x=2) +P(x=3)

= 8 C 0 0.7^0 0.3^8 + 8 C 1 0.7^1 0.3^7 + 8 C 2 0.7^2 0.3^6 + 8 C 3 0.7^3 0.3^5 + 8 C 4 0.7^4 0.3^4

= 0.1941

3. A study by a polling firm shows that 36.4% of women have a graduate degree.


a) For a randomly selected group of 325 women, find the mean and standard deviation for the number that have a graduate.

mean = np = 325* 0.364 = 118.3

s.d = sqrt( np ( 1-p) = sqrt( 325*0.364*(1-0.364) = 75.238

b)Based on this survey, would it be unusual to find that 100 have a graduate degree? (Explain your answer.)

yes

mean is more than 100 means we 118 women having probablity of having graduate.

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