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In: Statistics and Probability

Use the empirical rule to solve the problem. The amount of jen's monthly phone bill is...

Use the empirical rule to solve the problem. The amount of jen's monthly phone bill is normally distributed with a mean of $55 and a standard deviation of $12. What percentage of her phone bills are between $19 and $9?

Expert Solution

SOLUTION:

From given data,

Use the empirical rule to solve the problem. The amount of jen's monthly phone bill is normally distributed with a mean of $55 and a standard deviation of $12. What percentage of her phone bills are between $19 and $9

mean = = 55

standard deviation = =12

Let, a random variable X denotes the amount of jen's monthly phone bill (In $)

& X N ($55 , ($12)²)

Let ,

z = (x-) / N (0,1)

We have to find percentage of her phone bill are between $19 and $9

P(19 < x < 9) = P(19- / < x - / < 9- / )

= P(19- 55 /12 < Z < 9- 55 /12 )

= P(-3 < Z < -3.83 )

= P(Z < -3.83 ) - P(Z < -3 )

= 0.00006-0.00135

= -0.00129

The percentage of jen's phone bills are between $19 and $9 is

= 100*(-0.00129)

= - 0.129 %

orchestra answered 2 years ago

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