Question

In: Statistics and Probability

If you have 80 students in an introductory biology statistics class and only 70 are biology...

If you have 80 students in an introductory biology statistics class and only 70 are
biology students, then:
(a) Compare the probabilities that you will get no biology students in a random
sample of size 6 when you sample with and without replacement.
(b) Compare the probabilities that you will get all biology students in a random
sample of size 6 when you sample with and without replacement.
(c) Compare the probabilities that you will get 14 biology students and 2 non-
biology students in a sample of size 16 when you sample with and without
replacement.

Solutions

Expert Solution

Total number of students = 80

Number of Biology students = 70

Number of non-Biology students = 80-70=10

a) Sample with replacement. For each selection the number of non-biology students remain at 10 and the total students remain at 80

Number of ways of selecting 6 non-biology students from 10 is

Total number of ways of selecting 6 students from 80 is

the probabilities that you will get no biology students in a random sample of size 6 is same as

the probability that you select 6 non-biology students in a random sample of size 6

ans: the probabilities that you will get no biology students in a random sample of size 6, when you sample with replacement, is  0.0000038

Sample without replacement.

Number of ways of selecting 6 non-biology students from 10 is

Total number of ways of selecting 6 students from 80 is

the probability that you will get no biology students in a random sample of size 6 is same as

the probability that you select 6 non-biology students in a random sample of size 6

ans: the probability that you will get no biology students in a random sample of size 6, when you sample without replacement, is   0.00000070

b) Sample with replacement. For each selection the number of biology students remain at 70 and the total students remain at 80

Number of ways of selecting 6 biology students from 70 is

Total number of ways of selecting 6 students from 80 is

the probability that you will get all biology students in a random sample of size 6 is same as

the probability that you select 6 biology students in a random sample of size 6

ans: the probability that you will get all biology students in a random sample of size 6, when you sample with replacement, is   0.4488

Sample without replacement.

Number of ways of selecting 6 biology students from 70 is

Total number of ways of selecting 6 students from 80 is

the probability that you will get all biology students in a random sample of size 6 is same as

the probability that you select 6 biology students in a random sample of size 6

ans: the probability that you will get all biology students in a random sample of size 6, when you sample without replacement, is  0.4363

c) Sample with replacement. For each selection the number of biology students remain at 70 and the total students remain at 80

Number of ways of selecting 14 biology students from 70 and 2 non-biology from 10 is

But we can arrange these 14 biology and 2 non-biology in

ways

Number of ways of selecting and arrange 14 biology students from 70 and 2 non-biology from 10 is

Total number of ways of selecting 16 students from 80 is

the probabilities that you will get 14 biology students and 2 non-biology students in a sample of size 16 is

ans:  the probabilities that you will get 14 biology students and 2 non-biology students in a sample of size 16 , when you sample with replacement, is   0.2891

Sample without replacement.

Number of ways of selecting 14 biology students from 70 and 2 non-biology from 10 is

Total number of ways of selecting 16 students from 80 is

the probabilities that you will get 14 biology students and 2 non-biology students in a sample of size 16 is

ans:  the probabilities that you will get 14 biology students and 2 non-biology students in a sample of size 16, when you sample without replacement, is  0.3226

orchestra answered 2 years ago
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