Purchase Solution

Normal Distribution and Probabilities in Industries

Not what you're looking for?

Ask Custom Question

Can you please assist with questions 6-11 and 6-17 putting the answers and solutions in an excel spread sheet.

6.11 ) Consider a random variable, z, that has a standardized normal distribution. Determine the following probabilities:
a) P(0<z<1.96)
b) P(z>1.645)
c) P(1.28<z<2.33)
d) P(-2<z<3)
e) P(z>-1)

6.17 ) Bowser Bites Industries (BBI) sells large bags of dog food to warehouse clubs. BBI uses an automatic filling process to fill the bags. Weights of the filled bag are approximately normally distributed with a mean of 50 kilograms and standard deviation of 1.25 kilograms.
a) What is the probability that a filled bag will weigh less than 49.5 kilograms?
b) What is the probability that a randomly sampled filled bag will weigh between 48.5 and 51 kilograms?
c) What is the minimum weight a bag of dog food could be and remain in the top 15% of all bags filled?
d) BBI is unable to adjust the mean of the filling process. However, it is able to adjust the standard deviation of the filling process. What would the standard deviation need to be so that no more than 2% of all filled bags weigh more than 52 kilograms?

See the attached file.

Attachments
Purchase this Solution
Solution Summary

Uses EXCEL worksheet functions NORMSDIST, NORMSINV to calculate normal distribution probabilities.

Solution Preview

Please see the attached Excel file:

6.11 ) Consider a random variable, z, that has a standardized normal distribution. Determine the following probabilities:

We will use EXCEL worksheet function NORMSDIST to calculate the probabilities

a) P(0<z<1.96)

Between z= 0 and 1.96

z1= 0
z2= 1.96
Cumulative Probability corresponding to z1= 0 is= 0.5 =NORMSDIST(0) 0r= 50.00%
Cumulative Probability corresponding to z2= 1.96 is= 0.975 =NORMSDIST(1.96) 0r= 97.50%

Therefore probability that the value of z will be between z1= 0.00 and z2= 1.96
is = 47.50% =97.5%-50.%

Answer: 47.50% or 0.475

b) P(z>1.645)

To the right of z= 1.645

z= 1.645
Cumulative probability corresponding to Z= 1.645 is 0.95 =NORMSDIST(1.645) 0r= 95.00%
Thus area to the left of z= 1.645 is 95.00%
Hence area to the right of z= 1.645 is 5.00% =100% - 95.%

Answer: 5.00% 0r 0.0500

c) P(1.28<z<2.33)

Between z= 1.28 and 2.33

z1= 1.28
z2= 2.33
Cumulative Probability corresponding to z1= 1.28 is= 0.8997 =NORMSDIST(1.28) 0r= 89.97%
Cumulative ...

Purchase this Solution
Free BrainMass Quizzes
Know Your Statistical Concepts

Each question is a choice-summary multiple choice question that presents you with a statistical concept and then 4 numbered statements. You must decide which (if any) of the numbered statements is/are true as they relate to the statistical concept.

Terms and Definitions for Statistics

This quiz covers basic terms and definitions of statistics.

Measures of Central Tendency

Tests knowledge of the three main measures of central tendency, including some simple calculation questions.

Measures of Central Tendency

This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.

View More Free Quizzes
Related BrainMass Solutions

  • Coefficient of variation, NPV, Normal Distribution

    In problem 5, if you were to choose between Alternatives B and C only, would you need to use the coefficient of variation? Why? 9. Waste Industries is evaluating a $70,000 project with the following cash flows.

  • Normal distribution problem

    One way to solve this problem is to evaluate P(X>0) and P(X<0) and see if the probabilities are the same. In each case, find the Z-score and then look up the probability in the standard normal table.

  • Binomial distribution

    What is the mean and standard deviation? Mean =np=200*0.60=120 Variance =np(1-p)=48 Standard deviation = = =6.928 b. Is this a situation in which binomial probabilities can be approximated by the normal probability distribution?

  • Statistics : Probability

    299534 Statistics Probability Question and Bowser Bites Industries Question 1 Consider a random variable, z, that has a standardized normal distribution. Determine the following probabilities: a. P(0 < z < 1.96) b. P(z > 1.645) c.

  • Indicated Probabilities Using A Normal Distribution Table

    170613 Indicated Probabilities Using A Normal Distribution Table Find the indicated probabilities using the standard normal distribution table. Please show detail of calculation.

  • Probabilities based on normal distribution

    348681 Probabilities based on normal distribution.

  • Comparing investment success probabilities

    This 400 word solution shows how to compare the success probabilities of the competing investments in part a assuming normal distributions and in part b assuming skewed distributions.

  • Statistics MCQ - Multiple Choice

    The sum of all probabilities in any discrete probability distribution is not always exactly one, since some of the probabilities may be slightly larger than one. ___ T/F 5.

  • GAUSSIAN DISTRIBUTION AND PROBABILITY

    Determine the following probabilities: Solution: The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.

View More Related Solutions