Use computer let x represent a binomial random variable with...

(Use computer) Let X represent a binomial random variable with n = 140 and p = 0.29. Find the following probabilities. (Round your final answers to 4 decimal places.) a. P(X ≤ 40) b. P(X = 30) c. P(X > 50) d. P(X ≥ 45)

Transcript

00:01 In this question, we have been given to calculate the value of probability such that the value of mean can be here written to be equals to, it is n times p and it will be here 140 multiplied with 0 .29 and this is here going to be 40 .6.

00:17 So, here we can say that the standard deviation value, let us write it is here going to be standard deviation and that will be under root of np and then it is here 1 minus p.

00:29 So, this very value is here going to come around under root of, we can say it will be here 140 multiplied with 0 .29 and then it is here 1 minus 0 .29.

00:40 So, if we simplify this very expression, then the value of standard deviation will be 5 .369 and hence we can say that in the first part of this very problem, it will be probability of x and then here it is less than equals to 40.

00:56 So, this is here going to be, let us write it will be probability of, we can say z and then here it is less than equals to 40 minus, it is 40 .6 and then here it is going to be 5 .3 and then it is here 69 and if we simplify this very problem, it will be probability of z and that is, we can say less than equals to negative 0 .0 and then it is here 186.

01:23 So, this very value will be 0 .49 and then here it is 26.

01:28 So, we can put this very answer inside the box and it will here look like this.

01:33 Now, let us see how we can obtain the answer for the second part and here in the second part, we can say that we are having the probability of x that is equals to 30.

01:42 So, it can be here written as probability of, it will be here, so we are using the continuity correction, so that will be 29 .5 and then it is here minus 40 .6 and then in the denominator, it will be, let us write it is 5.

01:58 And then it is here 369.

02:00 Now, it is here z and then it will be here lesser than 30 .5 minus it is here going to be 40 .6 divided by it is 5 .3 and then here it is 69 and if we simplify this very problem, it will be here equals to, let us write it is probability of x is equals to 30 and it will be here probability of negative 2 .0674 and this is here z and now it will be here, we can say it is going to be lesser than and then it is negative 1 .88 and then it is 1 .2...

Question

(Use computer) Let X represent a binomial random variable with n = 140 and p = 0.29. Find the following probabilities. (Round your final answers to 4 decimal places.) a. P(X ≤ 40) b. P(X = 30) c. P(X > 50) d. P(X ≥ 45)

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