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(THE PROBABILITIES ABOUT X) : Set up and ind the indicated probability; a diagram is recommended....

(THE PROBABILITIES ABOUT X) : Set up and ind the indicated probability; a diagram is recommended.

4.) The average age of a vehicle registered in the United States is 8 years, or 96 months. Assume the standard deviation is 16 months. If a random sample of 36 vehicles is selected, ind the probability that the mean of their age is between 90 and 100 months.

Solutions

Expert Solution

Solution :

Given that,

mean = = 96

standard deviation = = 16

n=36

= 96

=  / n = 16 / 36=2.67

= P(90<    < 100) = P[(90-96) / 2.67< ( - ) / < (100-96) / 2.67)]

= P( -2.25< Z <1.50 )

= P(Z <1.50 ) - P(Z < -2.25)

Using z table,  

= 0.9332-0.0122

probability = 0.9210

milcah answered 8 months ago
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