menu
bartleby
search
close search
Hit Return to see all results

The Lakeside Coffee Shop morning customer load follows a normal distribution. The mean number of customers is 60 and the standard deviation is 15.Determine the probability that the number of customers tomorrow will be 50. If the store gets more than 70 customers, they need to have a fourth staff member working. What is the probability that they will need that fourth person tomorrow?If the number of customers falls below 42, then two staff members are sufficient. What are the chances only two workers are required tomorrow?

Question

The Lakeside Coffee Shop morning customer load follows a normal distribution. The mean number of customers is 60 and the standard deviation is 15.

  1. Determine the probability that the number of customers tomorrow will be 50. 
  2. If the store gets more than 70 customers, they need to have a fourth staff member working. What is the probability that they will need that fourth person tomorrow?
  3. If the number of customers falls below 42, then two staff members are sufficient. What are the chances only two workers are required tomorrow?
check_circleAnswer
Step 1

The normal distribution:

A continuous random variable X is said to follow normal distribution if the probability density function of X is,

fullscreen
Step 2

a.

Find the probability that the number of customers tomorrow will be 50:

Consider the variable lakeside coffee shop morning customer load as X.

It is given that the variable lakeside coffee shop morning customer load X is normally distributed.

Here, the mean number of customers is μ = 60 and standard deviation is σ = 15.

The given requirement is that the, number of customers tomorrow should be 50. That is, X = 50.

An important property of continuous distribution:

The probability of a continuous random variable can be calculated for any given interval within the range of values of the random variable. The PDF, f (X) of a continuous random variable gives the “density” of the probabilities about the value X. It does not, at all, indicate the exact probability of the value X of the continuous random variable.

As the continuous random variable can take an infinite number of values within a given range, the probability of taking one particular value within the range is practically 0.

Hence, probability that the number of customers tomorrow will be 50 will be 0, that is, the probability that the continuous normal random variable X will take exactly the value 50 is P(X = 50) = 0.

Thus, the probability that the number of customers tomorrow will be 50 is 0.

Step 3

b.

Find the probability that the lakeside coffee shop need fourth staff person tomorrow:

It is given that the lakeside coffee shop need fourth staff person if the number of customers to the shop exceeds 70.

The given requirement is that ...

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Our solutions are written by experts, many with advanced degrees, and available 24/7

See Solution
Tagged in

Math

Statistics

Other

Related Statistics Q&A

Find answers to questions asked by student like you

Show more Q&A add
question_answer

Q: Find the standard deviation for the group of data items. 5,5,5,5,7,9 ​(Simplify your answer. Rou...

A: Solution:Computation of standard deviation:Standard deviation for the group of data items is calcula...

question_answer

Q: Monica, still, takes one hour to wash a car and Bill takes two hours to wash a car.  If they work to...

A: Let Monica and Bill can complete the work in x hours if they work together.Washing a car can be deno...

question_answer

Q: A car dealer wants to get information about the number of years car owners keep their cars. A random...

A: Here, µ be the true population mean and n is the sample size.The (1-α) % confidence interval for pop...

question_answer

Q: Which is not one of the major assumptions typically associated with parametric tests of significance...

A: Introduction:Some of the major requirements (though not the only requirements and may vary from one ...

question_answer

Q: You are the foreman of the Bar-S cattle ranch in Colorado. A neighboring ranch has calves for sale, ...

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,...

question_answer

Q: Can a low barometer reading be used to predict maximum wind speed of an approaching tropical cyclone...

A: In this question we have the data, using which we have to plot the scatter plot and best line of fit...

question_answer

Q: A population has a mean of 15 and standard deviation of 3. Round the answers to two decimal places a...

A: Let X be the observation. X follows normal distribution with mean μ = 15 and the standard deviation ...

question_answer

Q: A study was done to look at the relationship between number of lovers college students have had in t...

A: The estimated regression line is as follows:

question_answer

Q: The state superintendent of schools consistently states that the average salary of all substitute te...

A: Hello. Since your question has multiple sub-parts, we will solve the first three sub-parts for you. ...

Sorry about that. What wasn’t helpful?