Statistical Distributions

Question 1

When can you model a variable using a binomial distribution?

Answer 1

1. There are a fixed number of trials.
2. There are two possible outcomes.
3. There is a fixed probability of success.
   4, The trials are independent of each other.

Question 2

The probability that a randomly chosen member of a reading group is left-handed is 0.15. A random sample of 20 members of the group is taken.
a) Suggest a suitable model for the random variable X, the number of members in the sample which are left-handed. Justify your choice.

Answer 2

There are only two possible outcomes, left-handed and right-handed. There are a fixed number of trials, 20. There is a fixed probability of success, 0.15. Assuming each member of the sample is independent a suitable model is X=B( 20, 0.15)

Question 3

The probability that a randomly chosen member of a reading group is left-handed is 0.15. A random sample of 20 members of the group is taken.
b) (i) Use the model to calculate the probability that exactly 7 members in the sample are left-handed.

Question 4

The probability that a randomly chosen member of a reading group is left-handed is 0.15. A random sample of 20 members of the group is taken.
b) (i) Use the model to calculate the probability that fewer than two members in the sample are left-handed.

Question 5

What does P( X is less than and equal to x) mean in cumulative probabilities?

Answer 5

The sum of all the individual probabilities up to and including x.

Question 6

What does P( X is greater than and equal to x) mean in cumulative probabilities?

Answer 6

The sum of all the individual probabilities greater than and including x.

Question 7

What does P( X is less than x) mean in cumulative probabilities?

Answer 7

The sum of all the individual probabilities is not greater than x.

Question 8

What does P( X is greater than x) mean in cumulative probabilities?

Answer 8

The sum of all the individual probabilities is not greater than x.