Question

Use the appropriate normal distribution to approximate the resulting binomial distributions. A convenience store owner claims that 55% of the people buying from her store, on a certain day of the week, buy coffee during their visit. A random sample of 35 customers is made. If the store owner's claim is correct, what is the probability that fewer than 23 customers in the sample buy coffee during their visit on that certain day of the week? a) 0.8238 b) 0.8643 c) 0.8980 d) 0.8790 e) 0.9082 f) None of the above.

          Use the appropriate normal distribution to approximate the resulting binomial distributions. A convenience store owner claims that 55% of the people buying from her store, on a certain day of the week, buy coffee during their visit. A random sample of 35 customers is made. If the store owner's claim is correct, what is the probability that fewer than 23 customers in the sample buy coffee during their visit on that certain day of the week?

a) 0.8238
b) 0.8643
c) 0.8980
d) 0.8790
e) 0.9082
f) None of the above.

Show more…

Use the appropriate normal distribution to approximate the resulting binomial distributions. A convenience store owner claims that 55% of the people buying from her store, on a certain day of the week, buy coffee during their visit. A random sample of 35 customers is made. If the store owner's claim is correct, what is the probability that fewer than 23 customers in the sample buy coffee during their visit on that certain day of the week?

a) 0.8238
b) 0.8643
c) 0.8980
d) 0.8790
e) 0.9082
f) None of the above.

Added by Joseph C.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert David Nguyen

07/22/2022

Step 1

The mean (μ) of a binomial distribution is np, and the standard deviation (σ) is sqrt(np(1-p)), where n is the number of trials and p is the probability of success. In this case, n = 35 (the number of customers) and p = 0.55 (the probability that a customer buys Show more…

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Transcript

00:01 Hi, i'm david and i'm here to have you answered your question.

00:03 Now let me bring up your question here.

00:06 In the question here we are going to discuss about the binomial approximation to the normal.

00:11 Let me remind you that if the x -10 follows by the binomial with the n and the b, then we can approximate the x by the normal, where we have the mean equal to n times b, standard division equal to the square root of the n times b, times 1 minus b.

00:28 And because it follows by the normal, it will tell you, the x we minus the mean of a standard division we obtained the standard no more.

00:36 In the question here we're given the p equal to the 0155 and we're given the n equal to the 35 and here we see the x you could follow by the binomial with the n equal to the 35 p equal to the zobon 55 and the question asks you a present the probability that fewer than 20 customer so x will be smaller than the 20 to find this probability first of all we need to apply the continuity correction to approximate addition to the probability this one will be the left 10 will be the plus 0 .5 into the 20 so it will be the x smaller than the 20 .5 the next time we need to confirm the x into the z to do it i apply this formula here.

01:31 To apply this formula, i need to know the mean first, mule equal to the n times b.

01:38 Now n equal to the 35 b equal to the 0155 and then we get equal to 25 times 0 .55 equal to the 19 .25 standard division by the formula equal to square root of the n times b times 1 minus b equal to the square root of the 35 times 0 .55 times 1 minus 0 .55 and if we compute we get equal to the 0 .45 and then taking the square root equal to the 2 .943.

02:16 Now we are ready to approximate this into the z.

02:19 If we apply this formula we will have the 20 .5 we minus the mean.

02:24 Will be the 19 .25 over the 2 .943 and if we compute we have the z will be smaller than the 20 .5 minus the 19 .25 divided by the answer equal to the 0 .42.

02:43 Now to find this probability i need to bring up the z table.

02:46 Let me copy the the table and i will put the table on the right here...

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