Customers arrive at a grocery store at an average of 2.2 per minute. Assume that the number of arrivals in a minute follows the Poisson distribution. Provide answers to the following to 3 decimal places.

Part a)

What is the probability that exactly two customers arrive in a minute?



Part b)

Find the probability that more than three customers arrive in a two-minute period.



Part c)

What is the probability that at least seven customers arrive in three minutes, given that exactly two arrive in the first minute?

Question 1: Motherboard can be ordered in lots of 1, 2, or 3 units. The random variable is the number of units ordered by a customer with the following probability mass function:

1. Find the value of k.
2. Calculate the probability of between 3 and 5 (inclusive) units are ordered.
3. Calculate the probability of more than 3 units are ordered.
4. Calculate the mean and standard deviation of the distribution

Consider the endothermic reactions in the last exercise. A total of 20 independent reactions are to be conducted.

(a) What is the probability that exactly 12 reactions result in a final temperature less than 272?

(b) What is the probability that at least 19 reactions result in a final temperature less than 272?

(c) What is the probability that at most 18 reactions result in a final temperature less than 272?

(d) What is the expected number of reactions that result in a final temperature of less than 272?

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 150lb and 201lb. The new population of pilots has normally distributed weights with a mean of 158lb and a standard deviation of 34.2 lb.

a. If a pilot is randomly​ selected, find the probability that his weight is between 150lb and 201lb.

b. if the number different pilots are randomly selected, find the probability that their mean weight is between 150lb and 201lb

c. When redesigning the ejection seat, which probability is more relevent ?

1. Consider the experiment of first drawing one card from a single suit and then rolling a single die

a. How many simple events are possible ?

b. List the out sample space .

c. What is the probability of picking the same value card as die roll ?

d. What is the probability of picking a different number card than value rolled ?

e. What is the probability of obtaining a combined value of less than ten (assume that face cards are worth 10 and the ace is worth 11

The number of contaminants in samples of one cubic centimetre of polluted water has a Poisson distribution with a mean of 1.

a. What is the probability a sample will contain some (one or more) contaminants?

b. If four samples are independently selected from this water, find the probability that at least one sample will contain some (one or more) contaminants?

c. If 100 samples are selected instead, what is approximately the probability of seeing at least 60 samples with a contaminant? (Use the Normal table provided for your calculations)

A telemarketer knows that, on average, he is able to make three sales in a 45-minute period. Suppose the number of sales he can make in a given time period is Poisson distributed.

a) What is the probability that he makes two sales in a 30 -minute period?

b )What is the probability that he makes at least two sales in a 30-minute period?

c) What is the probability that he makes only one sale in an hour-long period?

Please provide good explanation.

3The table below shows the number of diapers demanded daily and the cumulative probabilities associated with each level of demand. Daily Demand 1 2 3 Cumulative Probability 0.12 0.25 1 If a random number 67 is generated. What would be the simulated demand ?

1- Medical oxygen tanks carried by paramedics and used in hospitals contain a higher concentration of carbon dioxide than normal air. Explain the effect of this extra CO2 on a person being treated and the medical reason for this effect.

2- Most doctors agree that after a person quits smoking, the deposits in their lungs will be removed after a period of time, depending on how long the person smoked. What mechanism removes these deposits?