The average lifetime of a light bulb is 2850 hours with a standard deviation of 400....

The average lifetime of a light bulb is 2850 hours with a standard deviation of 400. A simple random sample of 30 bulbs is taken. What is the probability that the average life in the sample will be between 2600 and 2700 hours?

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Expert Solution

Solution :

Given that ,

mean = = 2850

standard deviation = =400

n = 30

= 2850

= / $\sqrt$ n= 400 / $\sqrt$ 30=73.0297

P(2600< < 2700) = P[(2600-2850) / 73.0297 < ( - ) / < (2700-2850) / 73.0297 )]

= P(-3.42 < Z <-2.05 )

= P(Z <-2.05 ) - P(Z <-3.42 )

Using z table

=0.0202-0.0003

=0.0199

probability= 0.0199

orchestra answered 1 year ago

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