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hi this is my last question for the month but i really need help on these 3 prob

ID: 3072916 • Letter: H

Question

hi this is my last question for the month but i really need help on these 3 problems, if theres anyway for you to help with 3 i would really really appreciate it!!

1.Suppose a drug test is 98% sensitive and 96% specific. That is, the test will produce 98% true positive results for drug users and 96% true negative results for non-drug users. Suppose that 2.4% of people are users of the drug. If a randomly selected individual tests positive, what is the probability he or she is a user?

Put your answer in percentage form (e.g. 10.91 not 0.1091) and then round to two decimal places. Do not include a % sign.

2. Suppose that I roll 18 six-sided dice and add the results together. What is the standard deviation of the distribution of possible outcomes?

Round your answer to two decimal places

3. In a small town there are 645 men and 503 women. In that town, there are 260 people over the age of 50, among which 144 are men. You meet a random person from this town. What is the probability that they are a woman over the age of 50?

Put your answer in percentage form (e.g. 10.71 not 0.1071) and then round to two decimal places. Do not include a % sign.

Explanation / Answer

1)

here P(tested positive)=P(user and tested positive)+P(not user and tested positive)

=0.024*0.98+(1-0.024)*(1-0.96) =0.06256

hence P(user|tested positive)=P(user and tested positive)/P((tested positive)

=0.024*0.98/0.06256=0.3760 ~ 37.60%

2)

for single die ; probability of an outcome p=1/6

hence E(X)=(1/6)*(1+2+3+4+5+6)=3.5

E(X2)=(1/6)*(12+22+32+42+52+62)=15.17

hence std deviation of single outcome =(E(X2)-(E(X))2)1/2 =1.7078

hence std deviation of sum on 18 six-sided dice =1.7078*sqrt(18)=7.25 (try 7.24 if this comes wrong)

3)

robability that they are a woman over the age of 50 =(260-144)/(645+503)=0.1010~ 10.10%