7. The following statements are true for a binomial distribution except:
(a) Binomial is a continuous probability distribution.
(b) There are n number of trials.
(c) There are two possible outcomes for each trial: Success (S) and Failure (F).
(d) The trials are independent of each other.
(e) The probability of success remains constant.
8. A salesperson for a company visits 6 accounts every day. From the past experience it is
known that the probability of selling an account is 35%. The probability that on a given
day the salesperson will sell at least one account is:
(a) 0.0743
(b) 0.9246
(c) 0.8319
(d) 0.3562
(e) 0.9087
9. A salesperson for a company visits 5 accounts every day. From the past experience it is
known that the probability of selling an account is 40%. The probability that on a given
day the salesperson will sell less at most two accounts is:
(a) 0.3602
(b) 0.5543
(c) 0.6826
(d) 0.5443
(e) 0.5282
10. Suppose that 3% of all packages mailed through ‘We Deliver Next Day’ delivery service do
not make to their destination the next day. The probability that exactly two packages do
not make to their destination in a sample of 10 selected packages is
(a) 0.0306
(b) 0.0015
(c) 0.0042
(d) 0.0153
(e) 0.0317
Hdje
7. The correct statement for a binomial distribution is:
(a) Binomial distribution is a discrete probability distribution, not a continuous one. It deals with a fixed number of discrete trials.
To understand why, let's break down the options:
- (a) is incorrect because binomial distribution deals with discrete events, such as the number of successes out of a fixed number of trials.
- (b) is correct because binomial distribution involves a fixed number of trials, denoted by 'n'.
- (c) is correct because binomial distribution assumes two possible outcomes for each trial: success (usually denoted by 'S') and failure (usually denoted by 'F').
- (d) is correct because binomial distribution assumes that the trials are independent of each other, meaning that the outcome of one trial does not affect the outcome of another trial.
- (e) is correct because binomial distribution assumes a constant probability of success for each trial.
8. To find the probability that the salesperson will sell at least one account, we can use the concept of binomial distribution. In this case, the salesperson visits 6 accounts every day, and the probability of selling an account is 35%.
The probability of selling at least one account can be calculated using the complement rule, which states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring.
Using the binomial probability formula, the probability of the salesperson not selling any accounts in one day is given by:
P(X = 0) = (6 choose 0) * (0.35^0) * (0.65^6) = 0.65^6
To find the probability of selling at least one account, we can subtract this probability from 1:
P(X >= 1) = 1 - P(X = 0) = 1 - (0.65^6)
Calculating this probability will give us the answer.
9. Similar to the previous question, we can use the concept of binomial distribution to find the probability that the salesperson will sell at most two accounts.
The probability of selling at most two accounts can be calculated by summing the probabilities of selling 0, 1, and 2 accounts.
To find the individual probabilities, we can use the binomial probability formula:
P(X = k) = (n choose k) * (p^k) * ((1-p)^(n-k))
We need to sum P(X = 0), P(X = 1), and P(X = 2) to get the probability of selling at most two accounts on a given day.
10. For this question, we have a fixed probability of 3% (or 0.03) for a package not making it to its destination the next day. We need to find the probability that exactly two packages do not make it to their destination in a sample of 10 selected packages.
We can use the binomial probability formula to calculate this probability:
P(X = k) = (n choose k) * (p^k) * ((1-p)^(n-k))
In this case, n = 10 (number of selected packages) and p = 0.03 (probability of a package not making it). We need to find P(X = 2) using this formula. Calculating this probability will give us the answer.