At QT Sugar factory the amounts which go into bag of sugar are supposed to be normallydistributed with mean 36 kg and standard deviation 0.1 kg. Once every 30 minutes a bag isselected from the production line, and its contents are noted precisely. If the amount of the baggoes below 35.8 kg or above 36.2 kg, then the bag will be declared out of control.a) If the process is in control, meaning u = 36 kg and o= 0.1 kg, find the probability that the bagwill be declared out of control.b) In the situation of (a), find the probability that the number of bag found out of control in aneight-hour day (16 inspections) will be zero.

Answered: Image /qna-images/answer/52307726-b85e-480d-8cf2-0418633ca3be.jpg

Answered: At QT Sugar factory the amounts which…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The products that a company is exporting in the United States have an average of 3 weeks lead time and a standard deviation of 0.5 week. Seven products are measured and assumed to be normally distributed, what percentage of the products have shorter lead time than 2.8 weeks?
Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2500 grams and a standard deviation of 700 grams while babies born after a gestation period of 40 weeks have a mean weight of 2700 grams and a standard deviation of 340 grams. If a 34-week gestation period baby weighs 2275 grams and a 40-week gestation period baby weighs 2475 grams, find the corresponding z-scores. Which baby weighs less relative to the gestation period?
The shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days. According to the Empirical Rule, about what percent of the products last between 0 and 3 days?
Suppose the systolic blood pressure (in mm) of adult males has an approximately normal distribution with mean u =125 and standard deviation o =14. Create an empirical rule graph with the following: • A title and label for the horizontal axis including units. • Vertical lines for the mean and first 3 standard deviations in each direction with numerical labels on the horizontal axis • Labels for the areas of the 8 regions separated by the vertical lines as well. Note: This may be hand drawn or computer generated. See the models for desired formats. a. Upload your completed file below. Choose File No file chosen Now use your graph to answer the following questions. b. About 68% of men will have blood pressure between what amounts? 111 and 139 c. What percentage of men will have a systolic blood pressure outside the range 97 mm to 139 mm? 18.5 d. Suppose you are a health practitioner and an adult male patient has systolic blood pressure of 168 mm. Use statistics to explain the gravity of…
A soft-drink machine is regulated so that it discharges an average of 200 mm/cup. If the amount of drink is normally distributed with a standard deviation equal to 15 mm, what fraction of the cups will contain more than 224mm?
Assume that a certain data is approximately bell-shaped with mean 91 and standard deviation 6. Use the Empirical Rule to find the percent of the data between 85 and 103. Show all the necessary calculations.
Suppose the heights of men are normally distributed with mean, μ = 69 inches, and standard deviation , σ = 3 inches. Suppose admission to a summer basketball camp requires that a camp participant must be in the top 10 % of men's heights, what is the minimum height that a camp participant can have in order to meet the camp's height admission requirement?
Assume that the weights of trout in a river are normally distributed. You randomly catch and weigh 20 such trout. The mean weight from your sample is 7.3 lb with a standard deviation of 0.9 lb. Test the claim that the mean weight of trout in this river is greater than 7 lb at a significance level of 0.01. Be sure to clearly identify your work, using appropriate notation at each step of the process, and summarize your final result in a complete sentence.
Suppose 140 geology students measure the mass of an ore sample. Due to human error and limitations in the reliability of the balance, not all the readings are equal. The results are found to closely approximate a normal curve, with mean 85 g and standard deviation 2 g. Use the symmetry of the normal curve and the empirical rule as needed to estimate the number of students reporting readings between 81 g and 89 g. The number of students reporting readings between 81 g and 89 g is (Round to the nearest whole number as needed.)
If batteries have lives that are normally distribute with mean 2, 800 hours and standard deviation 400 hours, using the 68-95-99.7 rule to approximate the percentage of batteries having a life less than 3, 600 hours.
During the busy season, it is important for the shipping manager at ShipMundo to be able to estimate the time it takes the loading crew to load a truck. The shipping manager has found that she can model the load times using a normal distribution with a mean of 152 minutes and a standard deviation of 15 minutes. Use this table or the ALEKS calculator to find the percentage of load times between 116 minutes and 149 minutes according to the model. For your intermediate computations, use four or more decimal places. Give your final answer to two decimal places (for example 98.23%).

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