Use the table of areas under the standard normal curve to...

Name: Use the table of areas under the standard normal curve to find the normal approximation for the probability of a binomial experiment of 55 successes in 240 trials, when p = 0.2. (Round your answer to four decimal places.)
Uploaded: 2022-12-08T16:12:05-08:00
Duration: 3 min 10 s
Channel: Sanchit Jain
Description: Use the table of areas under the standard normal curve to find the normal approximation for the probability of a binomial experiment of 55 successes in 240 trials, when p = 0.2. (Round your answer to four decimal places.)

Use the table of areas under the standard normal curve to find the normal approximation for the probability of a binomial experiment of 55 successes in 240 trials, when $p = 0.2$. (Round your answer to four decimal places.)

Transcript

00:01 Hello, students, we are going to write here, binomial experiment is given, find a normal approximation of the probability fewer than 65 successes in 190 trials.

00:12 So basically if i write here for this x here is a random variable which is binomially distributed having n comma p.

00:21 So let's erase this to make it more clear.

00:25 And value must be 190 having p value as 0 .4 so basically if i write here for this this must be this must be written as so basically here what happens is binomial binomial distribution distribution follows follows normal normal approximation here right here so we are going to calculate what would be our mu value this is np 190 multiplied by 0 .4 which is 76 and what would be our standard deviation sigma this this must be under root of under root of npqp is probability of success and this queue is probability of unsuccessful so we are going to write here this is 190 multiplied by 0 .4 multiplied by 0 .6 so basically we are going to write here for this this value must be written as under root of 45 .6 so let's erase this to make it more clear under root of 45 .6 so this final value would be written as we are going to write here this is 6 .75 so what we need here j score attribute must be calculated as x minus mu divided by sigma so x value is 65 minus mu mu is 76 divided by 6 .75 so we are going to calculate this 65 minus 76 that is 11 .11 divided by 6 .75 so this is minus 11 divided by 6 .75 that is minus 1 .63 so what we need fewer than this so it means that probability of z value is less than minus 1 .63 so basically if i write here for this from the z table we can easily conclude so this must be be equivalent to 0 .056 up to 4 decimal places.

02:50 This is 0 .056...

Question

Use the table of areas under the standard normal curve to find the normal approximation for the probability of a binomial experiment of 55 successes in 240 trials, when $p = 0.2$. (Round your answer to four decimal places.)

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