Question

In: Math

The life in hours of a 75-watt light bulb is known to be approximately normally distributed,...

The life in hours of a 75-watt light bulb is known to be approximately normally distributed, with standard deviation σ = 25 hours. A random sample of 62 bulbs has a mean life of x-bar = 1,014 hours. Construct a 98% confidence interval around the true population mean life of the light bulb.

Solutions

Expert Solution

Solution:-

98% confidence interval around the true population mean life of the light bulb is C.I = ( 1006.61, 1021.39).

n = 62, Mean = 1014, σ = 25

C.I = 1014 + 2.327*3.1750032

C.I = 1014 + 7.3882

C.I = ( 1006.61, 1021.39)


Related Solutions

Suppose the life span of a light bulb is normally distributed with mean 1000 hours and...
Suppose the life span of a light bulb is normally distributed with mean 1000 hours and standard deviation 75 hours. (a) Find the 57th percentile of this distribution. (b) Find the probability that a random light bulb will last longer than 1100 hours. (c) Find the probability that the life span of a light bulb will be more than 3.14 standard deviations away from the mean. (d) Suppose you take a sample of 15 light bulbs and measure the average...
1)The life in hours of a battery is known to be approximately normally distributed, with standard...
1)The life in hours of a battery is known to be approximately normally distributed, with standard deviation 1.25 hours. A random sample of 10 batteries has a mean life of 40.5 hours. A. Is there evidence to support the claim that battery life exceeds 40 hours ? Use α= 0.05. B. What is the P-value for the test in part A? C. What is the β-error for the test in part A if the true mean life is 42 hours?...
A 75 watt incandescent light bulb and an 18 watt compact fluorescent bulb are equally bright....
A 75 watt incandescent light bulb and an 18 watt compact fluorescent bulb are equally bright. How much warmer will an insulated closed 12 by 11 by 8.0 foot room get in 1.0 hour if it is lighted by an incandescent bulb than if it is lighted by a fluorescent bulb? At room temperature, the specific heat of air is 1.007 J/gC and its density is 1.2 g/L. The watt is the SI unit of power; 1 watt = 1...
True or False: The life in hours of a battery is known to be approximately normally...
True or False: The life in hours of a battery is known to be approximately normally distributed, with standard deviation of 15 hours. A random sample of 16 batteries has a mean life of 110 hours. Based on sampling results, there is sufficient evidence on this sample to support the claim that battery life exceeds 100 hours at α=0.05.
2. The lifetime of light bulb is normally distributed with mean of 1400 hours and standard...
2. The lifetime of light bulb is normally distributed with mean of 1400 hours and standard deviation of 200 hours. a. What is the probability that a randomly chosen light bulb will last for more than 1800 hours? b. What percentage of bulbs last between 1350 and 1550 hours? c. What percentage of bulbs last less than 1.5 standard deviations below the mean lifetime or longer than 1.5 standard deviations above the mean? d. Find a value k such that...
The lifetime of light bulb is normally distributed with mean of 1400 hours and standard deviation of 200 hours.
The lifetime of light bulb is normally distributed with mean of 1400 hours and standard deviation of 200 hours. a. What is the probability that a randomly chosen light bulb will last for more than 1800 hours? b. What percentage of bulbs last between 1350 and 1550 hours? c. What percentage of bulbs last less than 1.5 standard deviations below the mean lifetime or longer than 1.5 standard deviations above the mean? d. Find a value k such that 20% of the bulbs last...
The life in hours of a certain type of lightbulb is normally distributed with a known...
The life in hours of a certain type of lightbulb is normally distributed with a known standard deviation of 10 hours. A random sample of 15 lightbulbs has a sample mean life of 1000 hours. What would the 99% lower-confidence bound L on the mean life be, rounded to the nearest integer?
A power company manufactures a 100-watt light bulb that, according to the specifications written on the box, has a half-life of 900 hours with a standard deviation of 50 hours.
A power company manufactures a 100-watt light bulb that, according to the specifications written on the box, has a half-life of 900 hours with a standard deviation of 50 hours. At most, what percentage of the bulbs do not last at least 700 hours? Assume that the distribution is symmetric around the mean.
A light-bulb manufacturer advertises that the average life for its light bulbs is 900 hours. A...
A light-bulb manufacturer advertises that the average life for its light bulbs is 900 hours. A random sample of 15 of its light bulbs resulted in the following lives in hours.                          995 590 510 539 739 917 571 555                          916   728   664   693   708   887   849 At the 10% significance level, test the claim that the sample is from a population with a mean life of 900 hours. Use the P-value method of testing hypotheses. Identify the null and alternative hypotheses,...
The life in hours of a thermocouple used in a furnace is known to be approximately...
The life in hours of a thermocouple used in a furnace is known to be approximately normally distributed, with σ=20 hours. A random sample of 15 thermocouples resulted in the following data: 553, 552, 567, 579, 550, 541, 537, 553, 552, 546, 538, 553, 581, 539, 529. Is there evidence to support the claim that mean life exceeds 540 hours? Use a fixed-level test with =0.05. What is the P-value for this test? What is the -value for this test...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT