Question

According to a survey in a country, 35% of adults do not own a credit card suppose a simple random sample of 200 adus is obtained Complete parts a rough below (a) Descrbe the sampling distribution of the sample proportion of adults who do not own a credit card. Choose the phrase that best describes the shape of the sampling ontbution of below O A. Approximately normal because as 0.05N and p-p}<10 OB. Not normal because no 05 and 1- 2 10 O c. Approximately normal because no05N and np/t-ps2 10 OD. Not normal because no ON and nort-<10 Determine the mean of the sampling distribution of - (Round to two decimal places as needed) Determine the standard deviation of the samping distribution of 0.- (Round to three decimal places as needed) (D) What is the probably that in a random sample of 200 adults, more than 37 do not own a creat care The probati (Round to four decimal places as needed Interpret this probably it 100 dierent random samples of 200 adults were obtained one would expect to rest in more than 37 not owning (Round to the nearest Integer as needed) (e) What is the probability that in a random sample of 200 dus between 32 and 3 do not own area ? The probably Round to four decimal places as needed Interpret this probably 100 random samples of roots were and one wo r st in be d (c) What is the probability that in a random sample of 200 adults between 32 and 37 do not own a credit card The probabatys (Round to four decimal places as needed Interpret this probably if 100 different random samples of 200 adults were obtained one would expect to result in between and not owning a credit card (Round to the nearest wteger as needed) (d) Would it be unusual for a random sample of 200 muts to rest in 4 fewer who do not own act wh ere the correct choice (Round to four decimal placs as needed) O The rest is unusual because the probably that i s there the same proportions which is greater than 0 . The result is not unusual because the probatiaty that is less than or equal to the sample proportions which is less than on and the webox to complete you O OD The result is unusual because the probably that is less than or equal to the same proportions which is ess than The result is not unusual because the probaby that is less than or equal to the same proportions which is greater than Click to select your answers)

Answer 1

Given: p = 0.35

n = 200

(a) Approximately normal because n ≤ 0.05N and np(1 - p) ≥ 10

Mean of the sampling distribution of $\hat{p}$ , $\mu_\hat{p}$ = 0.35

Standard deviation of the sampling distribution of $\hat{p}$ ,

$\sigma_\hat{p}$ = = 0.034

p(1-p) V n

(b) The required probability = P($\hat{p}$ > 0.37)

= P{Z > (0.37 - 0.35)/0.034} = P(Z > 0.588)

= 0.2883​​​​​​

If 100 different random samples of 200 adults were obtained, one would expect 29 to result in more than 37% not owning a credit card

(c) The required probability = P(0.32 < $\hat{p}$ < 0.37)

= P(-0.882 < Z < 0.588)

= 0.5328

If 100 different random samples of 200 adults were obtained, one would expect 53 to result in between 32% and 37% not owning a credit card

(d) 64/200 = 0.32

Now, P($\hat{p}$ < 0.32) = 0.1789

The result is not unusual because the probability that $\hat{p}$ is less than or equal to the sample proportion is 0.1789 which is greater than 5%