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The life of a certain brand of battery is normally distributed, with mean 128 hours and standard deviation 16 hours. what is the probability that a battery you buy lasts at most 100 hours? standardize the variable. x = 100 is equivalent to z =

Respuesta :

-1.75 is the answer.

We have been given that

mean, [tex]\mu = 128[/tex]

standard deviation [tex]\sigma = 16[/tex]

[tex]x=100[/tex]

Let us evaluate the z score using the below mentioned formula

[tex]z=\frac{x-\mu}{\sigma}[/tex]

On substituting the given values, we get

[tex]z=\frac{100-128}{16} \\ \\ z=-1.75[/tex]

Thus, the value of z is -1.75.

Now, we find the probability that a battery you buy lasts at most 100 hours.

We will find the value for z= -1.75 using the z score table.

[tex]P(z=-1.75)= .04006[/tex]

Hence, the required probability is 0.04006


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