Statistics and Probability Answers

1. The Research & Development (R&D) team of a manufacturing firm discovered a new procedure that can be introduced into the production process that can substantially decrease production time. The firm has a limited fund allocated for process modifications that a standard is set for acceptability, that only a production time decrease of at least 8% is acceptable. Six production trials were undertaken showing a mean production time decrease of 8.4% with a standard deviation of 0.32%.
Using a level of significance of
(a) 0.01 and
(b) 0.05, test the hypothesis that the process should be introduced. Use t-distribution

Two types of chemical solutions treams, A and B, were tested for their alkalinity levels. Analysis of the 6 samples taken from solution A showed that the mean alkalinity level is 7.52 with a standard deviation of 0.024 while the 5 samples taken at Solution B showed an alkalinity level of 7.49 with a standard deviation of 0.032. Using a (a) 0.05 and (b) 0.01 significance level, determine whether the streams have different alkalinity levels. Use F-distribution.

The standard deviation of the annual precipitations of a region over a period of 100 years was 16 cm. During the last 15 years a standard deviation of annual precipitations was computed as 10 cm. Test the hypothesis that the precipitations in the region have become less variable than in the past, using a significance level of (a) 0.05 and (b) 0.01. Use chi-square distribution

1. The Research & Development (R&D) team of a manufacturing firm discovered a new procedure that can be introduced into the production process that can substantially decrease production time. The firm has a limited fund allocated for process modifications that a standard is set for acceptability, that only a production time decrease of at least 8% is acceptable. Six production trials were undertaken showing a mean production time decrease of 8.4% with a standard deviation of 0.32%.
Using a level of significance of
(a) 0.01 and
(b) 0.05, test the hypothesis that the process should be introduced. Use t-distribution

ose that the operation manager of computer package delivery service is contemplating the purchase of a new fleet of trucks. When packages are efficiently stored in the trucks in preparation for delivery, two major constraints have to be considered. The weight in pounds and volume in cubic feet for each item. Now suppose that in a sample of 200 packages the average weight is 26.0pounds with a standard deviation of 3.9 pounds. In addition suppose that the average volume for each of these packages is 8.8 cubic feet with standard deviation of 2.2 cubic feet. How can we compare the variation of the weight and volume

In a school group of 45 students, 37 did the Biology, Physics and 20 Math tasks. a) What is the probability that a student did the Math or Biology assignment? b) What is the probability that he did not do any of the three tasks?

A men’s shoe designer is willing to accommodate 95% of the male population. If the mean foot length is 25.25 cm and the standard deviation is 3.875 cm, answer the following

Q1. What is the smallest foot length the designed is willing to accommodate ?
Q2. What is the largest foot length the designed is willing to accommodate

A machine produces bottle caps. The machine is calibrated to produce bottle caps with a mean diameter of 2.8 cm and standard deviation of 0.03 cm. Let x represent the random variable for diameter of bottle caps. Leave your answers as a percent without rounding.

Q1. What percent of bottle caps are between 2.77cm and 2.83 cm?
Q2. Find P(2.74 ≤ x ≤ 2.86 ).
Q3. What percent of bottle caps are less than 2.71 cm?
Q4. Find P ( X ≥ 2.86 )
Q5. What percent of bottle caps are exactly 2.8 cm?
Q6. If all caps that are smaller than 2.71 cm and greater than 2.89 cm are rejected / thrown out, what percent would be lost ?

Classify each one as either True or False

Q1. The total area under a probability density polygon equals 1
Q2. The total area under the relative frequency polygon equals 1 when the interval size is 1
Q3. Smaller intervals sizes always allow you to get a smoother polygon that will better represent the data
Q4. The interval size is chosen when the difference between the polygon and the histogram bars is as small as possible
Q5. The interval size does not depend on the number of data points

Classify each of the following as a continuous or a discrete variable.

Q1. Heights of students in your class
Q2. Number of credits that students have at your school
Q3. Number of times you ride the bus each week
Q4. Time spent on the bus during a week
Q5. Speed of a cricket ball
Q6. Points scored in a soccer match
Q7. Length of a soccer field