The average life of a certain type of small motor is 10 years with a standard deviation of 2 years. The manufacturer replaces free all motors that fail while under guarantee. If he is willing to replace only 5% of the motors that fail, how long a guarantee should he offer? Assume that the lifetime of a motor follows a normal distribution.
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- The average life of a certain type of small motor is 10 years with a standard deviation of 2 years. The manufacturer replaces free all motors that fail while under guarantee. If he is willing to replace only 5% of the motors that fail, how long a guarantee should he offer? Assume that the lifetime of a motor follows a
normal distribution.
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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 __chicksAn oceanographer claims that the mean dive duration of a North Atlantic right whale is 11.3 minutes. A random sample of 34 dive durations has a mean of 12.4 minutes and a standard deviation of 2.2 minutes. At α=0.10 is there enough evidence to reject the oceanographer's claim? Complete parts (a) through (d) below. Assume the population is normally distributed. (a) Identify the claim and state H0 and Ha. (b) use technology to find the P value. Find the standardized test statistic, t. t=______ Obtain the P value P=_______ (c)Decide whether to reject or fail to reject the null hypothesis: (d) Interpret the decision in the context of the original claim:A company manufactures light bulbs. The company wants the bulbs to have a mean life span of 993 hours. This average is maintained by periodically testing random samples of 25 light bulbs. If the t-value falls between −t0.90 and t0.90, then the company will be satisfied that it is manufacturing acceptable light bulbs. For a random sample, the mean life span of the sample is 999 hours and the standard deviation is 23 hours. Assume that life spans are approximately normally distributed. Is the company making acceptable light bulbs? Explain. the company ___making acceptable light bulbs because t-value for the sample is t= and t0.90 = ( round two decimal places)
- 1- Let a coin and a die be tossed; let the sample space S consists of the twelve elements: S-{HI, H2, HЗ, Н4, H5, Н6, Т1, Т2, ТЗ, Т4, T5, Т6; (i) Express explicitly the following events: A={heads and an even number appear} B={a prime number appears} C={tails and an odd number appear} (ii) Express explicitly the event that: (а) А or B oссurs A or B Select one: О а. (Н2,НЗ,H5.T2,Т3,T5.Н4, Нб} O b. none O c. H2A company manufactures light bulbs. The company wants the bulbs to have a mean life span of 1002 hours. This average is maintained by periodically testing random samples of 16 light bulbs. If the t-value falls between −t0.99 and t0.99, then the company will be satisfied that it is manufacturing acceptable light bulbs. For a random sample, the mean life span of the sample is 1015 hours and the standard deviation is 24 hours. Assume that life spans are approximately normally distributed. Is the company making acceptable light bulbs? Explain. the company (is/is not) making acceptable lightbulbs because the t-value is t=___ and t0.99= ___The average prison sentence for a person convicted of second-degree murder is 16 years. If the sentences are normally distributed with a standard deviation of 2.1 years, find the following probabilities. A prison sentence is greater than 19 years. P(X>19) =
- 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 chicksAccording to an investment firm, the average 401(k) account balance was $99,000 in 2017. To test if this average has recently changed, suppose a sample of 30 401(k) plans was recently selected, and it was found that the average 401(k) balance was $109,676. Assume that the population standard deviation is $27,452. Using α=0.02, complete parts a through d.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/
- Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C.A single thermometer is randomly selected and tested. Let ZZ represent the reading of this thermometer at freezing. What reading separates the highest 8.92% from the rest? That is, if P(z>c)=0.0892P(z>c)=0.0892, find c.A company that makes cola drinks states that the mean caffeine content per 12-ounce bottle of cola is 40 milligrams. You want to test this claim. During your tests, you find that a random sample of thirty 12-ounce bottles of cola has a mean caffeine content of 38.9 milligrams. Assume the population is normally distributed and the population standard deviation is 7.3 milligrams. At α=0.09, can you reject the company's claim? Complete parts (a) through (e). (a) Identify H0 and Ha. Choose the correct answer below. A. H0: μ=40 Ha: μ≠40 B. H0: μ=38.9 Ha: μ≠38.9 C. H0: μ≠40 Ha: μ=40 D. H0: μ≤40 Ha: μ>40 E. H0: μ≤38.9 Ha: μ>38.9 F. H0: μ≠38.9 Ha: μ=The 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 dayschicks
