Question

The lifetimes of a certain brand of LED light bulbs are normally distributed with a mean of 53,400 hours and a standard deviation of 2500 hours.

A. If the company making these light bulbs claimed that they would last at least 50,000 hours. What proportion of light bulbs would meet the claim and last at least 50,000 hours? (12)

B. The company’s marketing director wants the claimed figure to be where 98% of these new light bulbs to last longer than the amount claimed by the company’s advertising? What number should be claimed so that 98% of the company’s new LEDlight bulbs meet the claim? (12)

C. If a random sample of 100 of these light bulbs is selected, what is the probability that the sample mean lifetime, ?̅, will be at least 53,000 hours? (12)

Answer #1

.The lifetimes of a certain brand of LED light bulbs are
normally distributed with a mean of 53,400 hours and a standard
deviation of 2500 hours.A.If the company making these light bulbs
claimed that they would last at least 50,000 hours. What proportion
of light bulbs would meet the claim and last at least 50,000 hours?
(12)B.The company’s marketing director wants the claimed figure to
be where 98% of these new light bulbs to last longer than the
amount claimed...

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 61
hours?
(b) What proportion of light bulbs will last 51 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...

Suppose that the lifetimes of light bulbs are approximately
normally distributed, with a mean of 56 hours and a standard
deviation of 3.2 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 52 hours or
less?
(c) What proportion of light bulbs will last between 59 and 62
hours?
(d) What is the probability that a randomly selected light...

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 61 hours? (b) What proportion of light bulbs will last
51 hours or less? (c) What proportion of light bulbs will last
between 59 and 62 hours? (d) What is the probability that a
randomly selected light bulb lasts...

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 61
hours?
(b) What proportion of light bulbs will last 51 hours or
less?
(c) What proportion of light bulbs will last between 58 and 62
hours?
(d) What is the probability that a randomly selected light bulb
lasts...

Suppose that the lifetimes of light bulbs are approximately
normally distributed, with a mean of 56 hours and a standard
deviation of 3.2 hours. With this information, answer the
following questions. (a) What proportion of light bulbs will last
more than 61 hours? (b) What proportion of light bulbs will last
50 hours or less? (c) What proportion of light bulbs will last
between 58 and 62 hours? (d) What is the probability that a
randomly selected light bulb lasts...

Suppose that lifetimes of light bulbs produced by a certain
company are uniformly distributed between 700 and 1100 hours. What
is the probability for a randomly selected 64 light bulbs that
total lifetime is at least 55600 hours?

LED light bulbs have an expected life that is exponentially
distributed with a mean of 5,000 hours. Determine the probability
that one these lights will last:
a- - At least 6,000 hours
b- - No longer than 1,000 hours
c- - Between 1,000 and 6,000 hours

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
question.
What proportion of light bulbs will last between 59 and 61
hours? (4 decimals)
What is the probablity that a randomly selected light bulb lasts
less than 45 hours? (4 decimals)

Suppose that lifetimes of light bulbs produced by a certain
company are uniformly distributed between 700 and 1100 hours. What
is the probability for a randomly selected 64 light bulbs that
total lifetime is at least 55600 hours? (use 4 digits after
decimal point) [hint: P(ΣX ≥
55600 hours)=?]

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