The manager of store A is aware that waiting times are much longer if the customer makes an order with a special request. From past experience this occurs 20% of the time. If we monitor the next 10 customers,
(a) What is the probability that half or more of these customers make a special request?
(b) What assumptions do you need to make to find this probability? Out of the next 100 customers,
(c) There is a probability of 90% that the number of customers make a special request equals or exceeds what value?
In: Statistics and Probability
Five males with an X-linked genetic disorder have one child each. The random variable x is the number of children among the five who inherit the X-linked genetic disorder. Determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied.
|
x |
P(x) |
|||
|---|---|---|---|---|
|
0 |
0.0320.032 |
|||
|
1 |
0.1630.163 |
|||
|
2 |
0.3050.305 |
|||
|
3 |
0.3050.305 |
|||
|
4 |
0.1630.163 |
|||
|
5 |
0.032 |
In: Statistics and Probability
Five males with an X-linked genetic disorder have one child each. The random variable x is the number of children among the five who inherit the X-linked genetic disorder. Determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied.
x P(x)
0 0.029
1 0.147
2 0.324
3 0.324
4 0.147
5 0.029
In: Statistics and Probability
We know that the population distribution for the number of hours that Americans sleep per night is normally distributed with a mean of 6.7 and a standard deviation of 1.4. a) What is the probability that a single, randomly draw observation (i.e., American) from this distribution sleeps less than 5 hours per night? b) What is the probability that a randomly drawn observation falls between 6 and 8 hours per night? c) What is the probability that a randomly draw observation is less than 7 hours per night?
In: Statistics and Probability
In: Statistics and Probability
If you randomly draw 3 marbels from a bag that contains 3 red
and 5 green marbles, without replacement. Denote by X the number of
red marbels drawn.
(a) What is the probability that exactly 1 red marbel is
drawn?
(b) Find the probability distribution of X.
(c) FInd the expected value and standard deviation of X.
(d) Draw the probability distribution of X and mark where the
expected value is and one standard deviation away from the mean in
both the positive and negative direction.
In: Statistics and Probability
Suppose you are testing products for defects and find that one in every 17 products exhibits a defect. Let T be the geometric RV modeling the number of products tested until a defect is found.
(a) What is the parameter q for T?
(b) Compute the probability that the first product tested exhibits a defect.
(c) Compute the probability that the first defective product is one of the first 10 tested.
(d) Compute the probability that the first defective product is not found until 8 or more products are tested.
In: Statistics and Probability
Suppose you are ordering pizza from a restaurant that is known to complete one order every 10 minutes. Let N be a Poisson RV modeling the number of orders completed in an hour.
(a) What is Λ?
(b) What is the probability that fewer than (or equal to) 5 orders are completed in one hour?
(c) What is the probability that between (or including) 4 to 8 orders are completed in an hour?
(d) What is the probability that more than (or equal to) 7 orders are completed in one hour?
In: Statistics and Probability
It is known that 40% of American Idol winners become famous. A sample of 50 American Idol winners are randomly selected.
(a) [1] What is the probability that exactly 25 of them become famous?
(b) [1] Find the probability that at least 20 of them become famous.
(c) [2] What is the probability that between 17 and 27 (including both 17 and 27) of them become famous.
(d) [2] Find the expected number of American Idol winners become famous in this sample and its standard deviation.
In: Statistics and Probability
Suppose you are ordering pizza from a restaurant that is known to complete one order every 10 minutes. Let N be a Poisson RV modeling the number of orders completed in an hour.
(a) What is Λ?
(b) What is the probability that fewer than (or equal to) 5 orders are completed in one hour?
(c) What is the probability that between (or including) 4 to 8 orders are completed in an hour?
(d) What is the probability that more than (or equal to) 7 orders are completed in one hour?
In: Statistics and Probability