Answer the following questions using the information shown below. Be sure to sho
ID: 466318 • Letter: A
Question
Answer the following questions using the information shown below. Be sure to show all your work.
Grizzly Clothes, a small Midwestern clothier, is considering fabricating a new line of men’s pants. It needs some help understanding its current male customer base in order to better assess what sizes of pants to offer. The firm presently has demographic data on all 5,000 of its male customers. It has found that the average weight of all its male customers is 195 lbs with a standard deviation of 20 pounds. In addition, the average weight has been found to be normally distributed. Listed below you will find weight information on just 20 randomly sampled customers.
*****PLEASE ANSWER QUESTIONS 5-10(ANSWERS ARE PROVIDED FOR QUESTIONS 1-4*******
Customer Weight Customer Weight Customer Weight Customer Weight
1 200 lbs 6 239 lbs 11 201lbs 16 210 lbs
2 225 7 167 12 185 17 203
3 180 8 143 13 184 18 194
4 197 9 242 14 178 19 212
5 186 10 194 15 181 20 207
1. Determine the mean weight based upon the sample data.
Answer: 196.4
2. Using the population standard deviation, how many standard deviations away from the population mean is the smallest observation in the sample data above?
Answer: std deviation = 22.47
2.37 std deviations away from population mean
3. If you were to draw a random sample of 20 observations from the entire population of 5,000 customers, what is the likelihood (probability) that you would find a larger sample mean than the value you calculated in question 1?
Answer: 90% likelihood
4. Grizzly Clothes has conducted some analysis that reveals that approximately 5 percent of its customers have an average weight below 162 pounds. Based upon this information, in a randomly drawn sample of 1,000 customers, what percentage of customers could be expected to have an average weight below 160 pounds?
Answer: 0.01 or 1% of customers are expected to have an avg weight below 160
5. Based upon the population data, what percentage of customers would be expected to weigh above 230 pounds?
6. Based upon the population data, what is the weight value that you would expect only 25 percent of the customers to exceed?
7. Based upon the population data, what is the weight level that would you would expect 90 percent of the customers to exceed?
8. Based upon the population data, what percentage of customers would be expected to weigh between 170 and 230 pounds?
9. Grizzly Clothes has conducted some analysis in consideration of producing only certain sizes of pants as few customers weigh less 135 pounds nor more than 255. If Grizzly Clothes is considering a minimum pants size that would fit an average man of 140 pounds, how many of its customers would be expected to have a weight below this value?
10. If Grizzly Clothes chose to model the distribution of customer weights with the discrete distribution shown below, what is the probability of a customer having a weight 215 pounds or less?
weight % of customers weight % of customers
100 lbs - 135 lbs 0.13% 195 lbs - 215 lbs 34.13%
135 - 155 2.15% 215 - 235 13.59%
155 - 175 13.59% 235 - 255 2.15%
175 - 195 34.13% 255 lbs or more 0.13%
Explanation / Answer
Population data
Mean
195
lbs
std dev
20
lbs
n
5000
customers
5. Based upon the population data, what percentage of customers would be expected to weigh above 230 pounds?
x
230
x = mean + z* std dev
z
1.75
Probability
0.96
(as per standard normal table)
Hence, 96% of population weighs less than or equal to 230 lbs, hence the remaining 4% population will weigh above 230 pounds.
6. Based upon the population data, what is the weight value that you would expect only 25 percent of the customers to exceed?
for 25% customers to exceed the weight, 75% of customers will be less than or equal to the given weight
For 75% probability, z score is
0.67
(as per the standard normal table)
x = mean + z * std dev
x =
208.49
hence,
hence, 25% of customers will exceed 208.49 lbs of weight
7. Based upon the population data, what is the weight level that would you would expect 90 percent of the customers to exceed?
for 90 % customers to exceed a weight value, 10 % will be less than or equal to the given weight
z score for 0.10 probability
-1.28
x = mean + z * std dev
x =
169.37
Hence, 90% customers are expected to exceed 169.37 lbs
8. Based upon the population data, what percentage of customers would be expected to weigh between 170 and 230 pounds?
customers weighing less than equal to 170 lbs
x
170
z = (x - mean)/std dev
z =
-1.25
Probability
10.57%
customers weighing less than equal to 230 lbs
x
230
z =
1.75
Probability
95.99%
Hence percentage of customers weighing between 170 lbs and 230 lbs = 95.99% - 10.57%
Ans.
=
85.43%
Population data
Mean
195
lbs
std dev
20
lbs
n
5000
customers
5. Based upon the population data, what percentage of customers would be expected to weigh above 230 pounds?
x
230
x = mean + z* std dev
z
1.75
Probability
0.96
(as per standard normal table)
Hence, 96% of population weighs less than or equal to 230 lbs, hence the remaining 4% population will weigh above 230 pounds.
6. Based upon the population data, what is the weight value that you would expect only 25 percent of the customers to exceed?
for 25% customers to exceed the weight, 75% of customers will be less than or equal to the given weight
For 75% probability, z score is
0.67
(as per the standard normal table)
x = mean + z * std dev
x =
208.49
hence,
hence, 25% of customers will exceed 208.49 lbs of weight
7. Based upon the population data, what is the weight level that would you would expect 90 percent of the customers to exceed?
for 90 % customers to exceed a weight value, 10 % will be less than or equal to the given weight
z score for 0.10 probability
-1.28
x = mean + z * std dev
x =
169.37
Hence, 90% customers are expected to exceed 169.37 lbs
8. Based upon the population data, what percentage of customers would be expected to weigh between 170 and 230 pounds?
customers weighing less than equal to 170 lbs
x
170
z = (x - mean)/std dev
z =
-1.25
Probability
10.57%
customers weighing less than equal to 230 lbs
x
230
z =
1.75
Probability
95.99%
Hence percentage of customers weighing between 170 lbs and 230 lbs = 95.99% - 10.57%
Ans.
=
85.43%
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.