Question 6 7 pts according to admissions data from the...

Name: question 6 7 pts according to admissions data from the massachusetts institute of technology mit 41 of freshman applicants are admitted to the college if 33240 individuals applied to mit las 53686
Uploaded: 2022-09-07T20:01:14-08:00
Duration: 5 min 10 s
Channel: Robin Corrigan
Description: question 6 7 pts according to admissions data from the massachusetts institute of technology mit 41 of freshman applicants are admitted to the college if 33240 individuals applied to mit las 53686

Question 6 7 pts According to admissions data from the Massachusetts Institute of Technology (MIT), 4.1% of freshman applicants are admitted to the college. If 33,240 individuals applied to MIT last year, find the probability that at least 1,400 of them were admitted. Round your answer to 4 decimal places. Question6 7 pts According to admissions data from the Massachusetts Institute of Technology (MIT),4.1% of freshman applicants are admitted to the college.If 33,240 individuals applied to MIT last year, find the probability that at least 1,400 of them were admitted. Round your answer to 4 decimal places

Transcript

00:01 In this exercise, we are told that 44 % of recent college graduates plan on pursuing a college degree.

00:08 So that means for any individual recent graduate, this probability is 0 .44.

00:15 And now we consider a random sample of 26 recent college graduates.

00:21 And we're asked for probabilities that certain numbers of these 26 plan to pursue graduate degrees.

00:29 So let's first define a random variable x as the number who plan to pursue a graduate degree out of the sample of 26.

00:37 Now here each of these 26 recent graduates can be viewed as a bernoulli trial.

00:42 There's two outcomes of interest.

00:44 They either plan to pursue a graduate degree or not.

00:47 And since it's a random sample, their outcomes are independent.

00:51 The number of successes in a given number of independent brunuli trials is a binomial random variable.

00:57 So here x is a binomial based on 26 trials and probability of success.

01:02 0 .44.

01:06 The probability mass function for the binomial random variable is given by this formula.

01:23 Now we want the probability that no more than 7, this is for part a, the probability that no more than 7 plan to pursue a graduate degree.

01:33 So this is the probability that x is less than equal to 7.

01:41 Now we could use the probability mass function to solve this by doing this calculation for x equals 0 plus for x equals 0.

01:50 Equals 1 plus for x equals 2 and so on up to 7, which is a bit tedious, so let's use software for this one.

01:57 We can use excel...

Question

Please give Ace some feedback