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A new type of electronics flash for cameras will last an average of 5000 hours with a standard deviation of 500 hours. A company quality control engineer intends to select a random sample of 100 of these flashes and use them until they fail. What is the probability that the mean life time of 100 flashes will be less than 4928 hours

Sagot :

Cricetus

Answer:

"0.0749" is the correct solution.

Step-by-step explanation:

Given:

Mean,

[tex]\mu=5000 \ hours[/tex]

Standard deviation,

[tex]\sigma=500 \ hours[/tex]

Random sample,

[tex]n = 100[/tex]

∴ [tex]\mu_\bar x \ = \ \mu[/tex]

       [tex]=5000 \ hours[/tex]

Now,

⇒ [tex]\sigma_\bar x[/tex] = [tex]\frac{\sigma}{\sqrt{n} }[/tex]

        = [tex]\frac{500}{\sqrt{100} }[/tex]

        = [tex]50 \ hours[/tex]

hence,

The probability will be:

=  [tex]P(\bar X<4928)[/tex]

=  [tex]P(\frac{\bar x-\mu_ \bar x}{\sigma_x} < \frac{4928-5000}{50} )[/tex]

=  [tex]P(z<\frac{-72}{50} )[/tex]

=  [tex]P(z<-1.44)[/tex]

=  [tex]0.0749[/tex]

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