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According to a survey in a country, 18% of adults do not own a credit card. Suppose a simple random sample of 800 adults is obtained. Complete parts (a) through (d) below. Determine the mean of the sampling distribution of $\hat{p}$. $\mu_{\hat{p}} = $ 0.18 (Round to two decimal places as needed.) Determine the standard deviation of the sampling distribution of $\hat{p}$. $\sigma_{\hat{p}} = $ 0.014 (Round to three decimal places as needed.) (b) What is the probability that in a random sample of 800 adults, more than 21% do not own a credit card? The probability is 0.0161. (Round to four decimal places as needed.) Interpret this probability. If 100 different random samples of 800 adults were obtained, one would expect 2 to result in more than 21% not owning a credit card. (Round to the nearest integer as needed.) (c) What is the probability that in a random sample of 800 adults, between 15% and 21% do not own a credit card? The probability is (Round to four decimal places as needed.) 

          According to a survey in a country, 18% of adults do not own a credit card. Suppose a simple random sample of 800 adults is obtained.
Complete parts (a) through (d) below.
Determine the mean of the sampling distribution of $\hat{p}$.
$\mu_{\hat{p}} = $ 0.18 (Round to two decimal places as needed.)
Determine the standard deviation of the sampling distribution of $\hat{p}$.
$\sigma_{\hat{p}} = $ 0.014 (Round to three decimal places as needed.)
(b) What is the probability that in a random sample of 800 adults, more than 21% do not own a credit card?
The probability is 0.0161.
(Round to four decimal places as needed.)
Interpret this probability.
If 100 different random samples of 800 adults were obtained, one would expect 2 to result in more than 21% not owning a credit card.
(Round to the nearest integer as needed.)
(c) What is the probability that in a random sample of 800 adults, between 15% and 21% do not own a credit card?
The probability is 
(Round to four decimal places as needed.)
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According to a survey in a country, 18% of adults do not own a credit card. Suppose a simple random sample of 800 adults is obtained. Complete parts (a) through (d) below. Determine the mean of the sampling distribution of p̂. μp̂ = 0.18 (Round to two decimal places as needed.) Determine the standard deviation of the sampling distribution of p̂. σp̂ = 0.014 (Round to three decimal places as needed.) (b) What is the probability that in a random sample of 800 adults, more than 21% do not own a credit card? The probability is 0.0161. (Round to four decimal places as needed.) Interpret this probability. If 100 different random samples of 800 adults were obtained, one would expect 2 to result in more than 21% not owning a credit card. (Round to the nearest integer as needed.) (c) What is the probability that in a random sample of 800 adults, between 15% and 21% do not own a credit card? The probability is (Round to four decimal places as needed.)

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Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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KK Complete parts a through d below according to a survey in a country. 18% of adults do not own a credit card. Suppose a simple random sample of 800 adults is obtained. a) Determine the mean of the sampling distribution of p = 0.18. Round to two decimal places as needed. b) Determine the standard deviation of the sampling distribution of p = 0.18. Round to three decimal places as needed. c) What is the probability that in a random sample of 800 adults, more than 21% do not own a credit card? The probability is 0.161. Round to four decimal places as needed. Interpret this probability. d) If 100 different random samples of 800 adults were obtained, one would expect 2 to result in more than 21% not owning a credit card. Round to the nearest integer as needed. e) What is the probability that in a random sample of 800 adults, between 15% and 21% do not own a credit card? The probability is (to be determined). Round to four decimal places as needed.
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Transcript

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00:02 So in this question, what we have here is that indeed, we can use the normal distribution because the sample size that we are considering is less than 5 % of the total population size.
00:19 And when we count for the, in this case here, for this value, this is greater or equal than 10 for our case.
00:29 So that is true.
00:30 So we can use the normal distribution.
00:32 Or at least, a approximation to the normal distribution.
00:36 So now to find the mean of the p hat, this is equal to the true value of p, which is the 0 .21 related to the 21 % that they know.
00:47 Then the standard deviation here is given by the square root of this p, 1 minus p, divided by the sample size they collected.
00:57 So in this case, the sample size is 400, which is going to give us as the value for sigma 0 .02.
01:06 Then what we need to find is the probability that in this sample, more than 24 % does not own a credit card...
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