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A random sample of 100 articles taken from a batch of 2000 articles with S. D. 0.048 shows that the average diameter of
the articles is 0.354. Find 95% confidence interval for the average diameter of this batch of 2000 articles. (Given area
under the normal curve between and is 0.475)
Samples of certain size are drawn from a normally distributed population with S. D. 16. It is observed that the probability
of the sample mean lying between 9.8 and 14.6 is 45.14%. Find the sample-size and the population mean. (Given that
∫ ( )
The random variable X is normally distributed with mean 68 cm and 2.5 cm. What should be the size of the sample whose
mean shall not differ from the population mean by more than 1 cm with probability 0.95? (Given that area under standard
normal curve to the right of the ordinate at 1.96 is 0.025)
Samples of weights of 200 students each are drawn from a normal population of the weights of students with S.D. 10
pound. Variance in each sample is computed. Find (i) mean (ii) standard deviation of the sampling distribution of sample
variance.
The guaranteed average life of a certain type of electric light bulbs is 1000 hours with a standard deviation of 125 hours.
It is proposed to sample the output so as to assure that 90% of the bulbs do not fall short of the guaranteed average by
more than 2.5%. What should be the minimum size of the sample? (The area under standard normal curve from to
is 0.4)
mike christian decides to work for another company that will pay him 2,000 per week and 10% commission on sales above 20,000 for the week if he sold good worth costing 18,00 each?
Find the length of an arc in a circle of radius 10 centimeters subtended by the central angle of 50°. Show your work.
2. Graph on [-4π, 4π] and verbalize how the graph varies from the graphs of .
Graph on the window [−5π, 5π] and describe freely what the graph shows. You can use www.desmos.com/calculator to obtain the graphs.
3. A 23-ft ladder leans against a building so that the angle between the ground and the ladder is 80°. How high does the ladder reach up the side of the building? Show the steps of your reasoning.
Part 1
An elevator has a placard stating that the maximum capacity is 1376 lb—8 passengers. So, 8 adult male passengers can have a mean weight of up to 1376/8=172 pounds. If the elevator is loaded with 8 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 172 lb. (Assume that weights of males are normally distributed with a mean of 178 lb and a standard deviation of 27 lb.) Does this elevator appear to be safe?
Question content area bottom
Part 1
The probability the elevator is overloaded is
.
The furniture company inexpensive tables and chairs. The production process of each is similar in the painting department each table take 4 hours of carpentry and 2 hours in the painting department. Each chair requires 3 hours of carpentry and 1 hour painting department. During the current product period 240 hours of carpentry time are available and 100 hrs in the painting is available. Each table sold yields of profit of $7 and chair produced sold for $5 profit. Find the best combination of table and chairs to manufacture in order to reach the maximum number of profit?
Evaluate the following line integrals along with the curve C.
(a) ∫
C (x2 − 2y2 ) ds; C is the line segment parametrized by r(t) = < t / √ 2 , t / √ 2 >, for 0 ≤ t ≤ 4.
