Question 8 The lifetimes of interactive computer chips produced by a certain semiconductor manufacturer are normally distributed having mean 4.4 × 10° hours with a standard deviation of 3 x 10$ hours. a) If a mainframe manufacturer requires that at least 90 percent of the chips from a large batch will have lifetimes of at least 4.0 × 10° hours, should he contract with the semiconductor firm? b) What is the probability that a batch of 100 chips will contain at least 4 whose lifetimes are less than 3.8 ×10° hours?
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- The incubation time for a breed of chicks is normally distributed with a mean of 29 days and standard deviation of approximately 3 days. Look at the figure below and answer the following questions. If 1000 eggs are being incubated, how many chicks do we expect will hatch in the following time periods? (Note: In this problem, let us agree to think of a single day or a succession of days as a continuous interval of time. Assume all eggs eventually hatch.) (a) in 23 to 35 days __ chicks(b) in 26 to 32 days __chicks2. An automobile battery manufacturer claims that its midgrade battery has a mean life of 50 months with a standard deviation of 6 months. Suppose the distribution of battery lives of this particular brand is approximately normal. On the assumption that the claims are true, find the probability that a randomly selected battery of this type will last less than 48 months. (Use the software link for every question) (a) Let X = number of months a battery will last. Write the question above in terms of this variable X (b) Find the probability that a single battery of this type will last less than 48 months. (c) Find the probability that the mean of a random sample of 36 batteries will be less than 48 months. (d) Why do you think the values from part (b) and part (c) are different? Explain.An electrical engineer wishes to compare the mean lifetimes of two types of transistors in an application involving high-temperature performance. A sample of 60 transistors of type A were tested and were found to have a mean lifetime of 1827 hours and a standard deviation of 174 hours. A sample of 180 transistors of type B were tested and were found to have a mean lifetime of 1658 hours and a standard deviation of 231 hours. Let ux represent the population mean for transistors of type A and µy represent the population mean for transistors of type B. Find a 95% confidence interval for the difference uy – µy . Round the answers to three decimal places. The 95% confidence interval is
- Question 4 a) For a large group of sale prospects, it has been observed that 22 percent of those contacted personally by a sales representative will make a purchase. If a sales representative contacts 35 prospects: i) Determine the probability that 10 or more will make a purchase (include also correction of continuity). ii) Determine the probability that not more than 3 will make a purchase (include also correction of continuity). iii) In what condition does binomial distribution approximate to normal distribution?Water samples are taken from water used for cooling as it is being discharged from a power plant into a river. It has been determined that as long as the mean temperature of the discharged water is at most 150°F, there will be no negative effects on the river's ecosystem. To investigate whether the plant is in compliance with regulations that prohibit a mean discharge water temperature above 150°, 50 water samples will be taken at randomly selected times and the temperature of each sample recorded. The resulting data will be used to test the hypotheses Ho: μ = 150° versus H₂: μ > 150°. In the context of this situation, describe type I error. a A type I error occurs when our estimate for the mean discharge temperature is higher than the actual temperature. A type I error occurs when we say that the plant is not in compliance when in fact it is. A type I error occurs when our estimate for the mean discharge temperature is lower than the actual temperature. A type I error occurs when we…The incubation time for a breed of chicks is normally distributed with a mean of 29 days and standard deviation of approximately 3 days. Look at the figure below and answer the following questions. If 1000 eggs are being incubated, how many chicks do we expect will hatch in the following time periods? (Note: In this problem, let us agree to think of a single day or a succession of days as a continuous interval of time. Assume all eggs eventually hatch.) (a) in 23 to 35 days chicks(b) in 26 to 32 days chicks(c) in 29 days or fewer chicks(d) in 20 to 38 days chicks
- Suppose that the lifetimes of tires of a certain brand are normally distributed with a mean of 74,500 miles and a standard deviation of o miles. These tires come with a 55,000-mile warranty. The manufacturer of the tires can adjust o during the production process, but the adjustment of o is quite costly. The manufacturer wants to set ở once and for all so that only 1% of the tires will fail before warranty expires. Find the standard deviation to be set. Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place. | miles Check esc -> @ 23 24 4. 5 6 1 2 y e tab w/Each of the batteries in a collection of 40 batteries is equally likely to be either a type A or a type B battery. Type A batteries last for an amount of time that has mean 50 and standard deviation 15; type B batteries last for an amount of time that has mean 30 and standard deviation 6. (a) Approximate the probability that the total life of all 40 batteries exceeds 1700. (b) Suppose it is known that 20 of the batteries are type A and 20 are type B. Now approximate the probability that the total life of all 40 batteries exceeds 1700.Question 4 a) For a large group of sale prospects, it has been observed that 22 percent of those contacted personally by a sales representative will make a purchase. If a sales representative contacts 35 prospects: i) Determine the probability that 10 or more will make a purchase (include also correction of continuity). ii) Determine the probability that not more than 3 will make a purchase (include also correction of continuity). iii) In what condition does binomial distribution approximate to normal distribution?
- A supervisor at a local widget making company has been monitoring the output of one of the machines used to manufacture small aluminum plates. Past data indicate that if the machine is operating "properly," the length of the plates produced by this machine can be modeled as being normally distributed with a mean of 117 centimeters and a standard deviation of 5.2 centimeters. Suppose 16 plates produced by this machine are randomly selected. What is the probability that the average length of these 16 plates will be between 116 and 120 centimeters when the machine is operating "properly?" Z and t TABLES ARE GIVEN AS QUESTIONS 28-29. PLEASE SHOW ALL YOUR CALCULATIONS.CORRECT ANSWER WITHOUT CALCULATIONS WILL BE AWARDED PARTIAL CREDIT. Paragraph В IThe incubation time for Rhode Island Red chicks is normally distributed with a mean of 29 days and standard deviation of approximately 3 days. Look at the figure below and answer the following questions. If 1000 eggs are being incubated, how many chicks do we expect will hatch in the following time periods? (Note: In this problem, let us agree to think of a single day or a succession of days as a continuous interval of time. Assume all eggs eventually hatch.) (a) in 23 to 35 dayschicks(b) in 26 to 32 dayschicks(c) in 29 days or fewerchicks(d) in 20 to 38 dayschicksSuppose that the lifetimes of tires of a certain brand are normally distributed with a mean of 74.000 miles and a standard deviation ofo miles. These tires come with a 65,000-mile warranty. The manufacturer of the tires can adjust o during the production process, but the adjustment of o is quite costly. The manufacturer wants to set o once and for all so that only 2% of the tires will fail before warranty expires. Find the standard deviation to be set. Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place. | miles