Holooly Plus Logo
Holooly Plus Logo

Question 10.5: Customers arrive randomly at a supermarket at an average rat......

Customers arrive randomly at a supermarket at an average rate of 2.5 customers per minute, where the customer arrivals form a Poisson distribution. Determine the probability that:
1. No customers arrive in any particular minute
2. Exactly one customer arrives in any particular minute
3. Two or more customers arrive in any particular minute
4. One or more customers arrive in any 30-second period.

Step-by-Step
The 'Blue Check Mark' means that this solution was answered by an expert.
Learn more on how do we answer questions.
Report Answer

The mean λ is 2.5 per minute for parts 1–3 and λ is 1.25 for part 4.

  1. {P}(X=0)=e^{-2.5}*2.5^{0}/0!=0.0821
  2. {P}(X=1)=e^{-2.5}*2.5^{1}/1!=0.2052
  3. P(2 or more) = 1 − P(X = 0 or X = 1)] = 1 − [P(X = 0) + P(X = 1)] = 0.7127
  4. P(1 or more) = 1 − P(X = 0) = 1-e^{-1.25}*1.25^{0}/0!=1-0.2865=0.7134

Related Answered Questions

Question: 10.9

A new machine has been introduced and management is questioning whether it is more productive than the previous one. Management takes 15 samples of this week’s hourly output to test whether it is less productive, and the average production per hour is 1250 items with a standard deviation of 50. The ...

Verified Answer:

The sample mean is 1250, the population mean is 12...
Question: 10.8

Suppose three faulty components are identified in a random sample of 20 products taken from a production line. What statement can be made about the defect rate of all finished products? ...

Verified Answer:

The proportion of defective products in the sample...
Question: 10.6

Weights of bags of oranges are normally distributed with mean 3 lbs and standard deviation 0.2 lb. The delivery to a supermarket is 350 bags at a time. Determine the following: 1. Standardize to a unit normal distribution. 2. What is the probability that a standard bag will weigh more than 3.5 lbs? ...

Verified Answer:

1. Z = X − μ/σ = X − 3/0.2. 2. Therefore, when X =...
Question: 10.7

Suppose a new motor fuel has been tested on 30 similar cars, and the fuel consumption was 44.1 mpg with a standard deviation of 2.9 mpg. Calculate a 95% confidence interval for the fuel consumption of this model of car. ...

Verified Answer:

The sample mean is 44.1, the sample standard devia...
Question: 10.4

The probability that a printer will need correcting adjustments during a day is 0.2. If there are five printers running on a particular day determine the probability of: 1. No printers need correcting 2. One printer needs correcting 3. Two printers require correcting 4. More than two printers ...

Verified Answer:

There are five trials (with n = 5, p = 0.2, and th...
Question: 10.3

Approximately 1% of women have breast cancer (i.e., 99% do not) with 80% of mammogram tests detecting breast cancer when it is there (i.e., 20% miss it), and 9.6% of mammograms detect breast cancer when it is not there (false positive) with 90.4% correctly returning a negative). What is the ...

Verified Answer:

Let T be the event that the patient’s mammogram te...
Question: 10.2

A medical lab is 99% effective in detecting a certain disease when it is actually present, and it yields a false positive for 1% of healthy people tested. If 0.25% of the population actually have the disease, what is the probability that a person has the disease if the patient’s blood test is ...

Verified Answer:

Let T be the event that the patient’s test result ...
Question: 10.1

A family has two children. Find the probability that they are both girls given that they have at least one girl. ...

Verified Answer:

The sample space for a family of two children is S...