Trucks in a delivery fleet travel a mean of 80 miles per day with a standard deviation of 30 miles per day. The mileage per day is distributed normally. Find the probability that a truck drives between 97 and 107 miles in a day. (Round your answer to 4 decimal places)
Accepted Solution
A:
Answer: 0.1037Step-by-step explanation:Given : Mean : [tex]\mu=80\text{ miles per day}[/tex]Standard deviation : [tex]\sigma = 30\text{ miles per day}[/tex]The formula to calculate the z-score is given by :-[tex]z=\dfrac{x-\mu}{\sigma}[/tex]For x = 97 miles per day ,[tex]z=\dfrac{97-80}{30}\approx0.57[/tex]For x = 107 miles per day ,[tex]z=\dfrac{97-80}{30}=0.9[/tex]The P-value =[tex]P(0.57<z<0.9)=P(z<0.9)-P(z<0.57)[/tex][tex]=0.8159398-0.7122603=0.1036795\approx0.1037[/tex]Hence, the probability that a truck drives between 97 and 107 miles in a day = 0.1037