In: Statistics and Probability

An electrical firm manufacturers light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 48 hours. If a sample of 36 bulbs has an average life of 780 hours, find the bounds of a 99% confidence interval for the population mean of all bulbs produced by this firm.

780\pm3.29\cdot(8)

None of these

solution:

the length of life of bulb is approximately normally distributed with standard deviation hours.

a sample of n = 36 has a mean of hours

we need to find a 99% confidence interval for mean life of all bulb

confidence level = 99% = 0.99

since population standard deviation is known, so confidence interval would be

where is the z value having an area to the right

= = 2.575

so lower bound = 780 - 20.6 = 759.4

upper bound = 780 + 20.6 = 800.6

so 99% confidence interval for the mean life of all bulb would be (759.4, 800.6)

An electrical firm manufactures light bulbs that have a length
of life that is approximately normally distributed with a standard
deviation of 35 hours. If a sample of 50 bulbs has an average life
of 900 hours, find a 98% confidence interval for the population
mean of all bulbs produced by this firm.A properly labeled
figure of the normal distribution curve and x and/or z values is
required for each problem

An electrical firm manufactures light bulbs that have a length
of life that is approximately normally distributed with a standard
deviation of 40 hours. If a sample of 30 bulbs has an average life
of 780 hours, find a 95% confidence interval for the population
mean of all bulbs produced by this firm.
764.99 < µ < 795.008
768.02 < µ < 791.98
700.30 < µ < 859.70
765.69 < µ < 794.31

An electrical firm manufactures light bulbs that have a length
of life that is approximately normally distributed with an unknown
standard deviation. If a sample of 30 bulbs has an average life of
780 hours and a sample standard deviation of 50 hours, find a 95%
confidence interval for the population mean of all bulbs produced
by this firm.
761.33 < µ < 798.67
764.49 < µ < 795.91
765.07 < µ < 794.93
768.02 < µ < 791.98

An electrical firm manufactures light bulbs that have a length
of life that is approximately normally distributed with a standard
deviation of 40 hours. If a sample of 30 bulbs has a an average
life of 780 hours, find a 96% confidence interval for the
population mean of all bulbs produced by this firm.

An electrical firm manufacturers batteries that have a length of
life that is approximately normally distributed with a standard
deviation of 40 hours. If a sample of 64 batteries has an average
life of 780 hours, find the bounds of a 95% confidence interval for
the population mean of all batteries produced by this firm.

2. An electrical firm manufactures light bulbs that have a
lifetime that is approximately normally distributed with a standard
deviation of 35 hours. A lifetime test of n=25 samples resulted in
the sample average of 1007 hours. Assume the significance level of
0.05.
(a) Test the hypothesis H0:μ=1000
versus H1:μ≠1000 using a
p-value. (6 pts)
(b) Calculate the power of the test if the true mean lifetime is
1010. (8 pts)
(c) What sample size would be required to detect...

A company manufactures light bulbs. These light bulbs have a
length of life that is normally distributed with a known standard
deviation of 40 hours. If a sample of 36 light bulbs has an average
life of 780 hours, find the 95 percent confidence interval for the
population mean of all light bulbs manufactured by this
company.

Suppose that the lifetimes of light bulbs are approximately normally distributed, with a mean of 57 hours and a standard deviation of 3.5 hours. With this information, answer the following questions. (a) What proportion of light bulbs will last more than 60 hours? (b) What proportion of light bulbs will last 50 hours or less? (c) What proportion of light bulbs will last between 58 and 61 hours? (d) What is the probability that a randomly selected light bulb lasts less than 46 hours? (a)...

Suppose that the lifetimes of light bulbs are approximately
normally distributed, with a mean of 56 hours and a standard
deviation of 3.3 hours. With this information, answer the
following questions.
(a) What proportion of light bulbs will last more than
61hours?
(b) What proportion of light bulbs will last 51 hours or
less?
(c) What proportion of light bulbs will last between 57 and 62
hours?
(d) What is the probability that a randomly selected light bulb
lasts less...

Suppose that the lifetimes of light bulbs are approximately
normally distributed, with a mean of 57 hours and a standard
deviation of 3.5 hours. With this information, answer the
following questions. (a) What proportion of light bulbs will last
more than 60 hours? (b) What proportion of light bulbs will last
50 hours or less? (c) What proportion of light bulbs will last
between 57 and 61 hours? (d) What is the probability that a
randomly selected light bulb lasts...

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