According to a survey in a country, 25% of adults do not own a credit card. Supp

Question

According to a survey in a country, 25% of adults do not own a credit card. Suppose a simple random sample of 900 adults is obtained. Complete parts and show the work.

(b) What is the probability that in a random sample of 900 adults, more than 27% do not own a credit card?

(c) What is the probability that in a random sample of 900 adults, between 22% and 27% do not own a credit card?

(d) Would it be unusual for a random sample of 900 adults to result in 198 or fewer who do not own a credit card? Why? Select the correct choice below and fill in the answer box to complete your choice.

1. The result is not unusual because the probability that p^ is greater than or equal to this sample proportion is greater than 5%.

2. The result is not unusual because the probability that p^ is greater than or equal to this sample proportion is less than 5%.

3. The result is unusual because the probability that p^ is greater than or equal to this sample proportion is greater than 5%.

4. The result is unusual because the probability that p^ is greater than or equal to this sample proportion is less than 5%.

Explanation / Answer

here p=0.25

and n=900

hence std error =(p(1-p)/n)1/2 =0.0144

b) P(X>0.27)=1-P(X<0.27)=1-P(Z<(0.27-0.25)/0.0144)=1-P(Z<1.3856)=1-0.9171=0.0829

c)P(0.22<X<0.27)=P((0.22-0.25)/0.0144<Z<(0.27-0.25)/0.0144)=P(-2.0785<Z<1.3856)=0.9171-0.0188=0.8982

d)

here mean =np=900*0.25=225

and std deviation =(np(1-p))1/2 =12.99

hence P(X<=198)=P(Z<(198.5-225)/12.99)=P(Z<-2.04)=0.0207

hence option 4 is correct

4. The result is unusual because the probability that p^ is greater than or equal to this sample proportion is less than 5%.

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