In a large Biology class, the scores of the final exam were approximately normal

Question

In a large Biology class, the scores of the final exam were approximately normally distributed with mean 80.5 and standard deviation 9.9. What proportion of final exam scores were greater than 70.4? Write only a number as your answer. Round to decimal places (for example 0.0048). Do not write as a percentage. Your Answer: The lifetime of a certain type of automobile tire (in thousands of miles) is normally mean 43 and standard deviation 5. Find the percentile corresponding to p = 57 % of the time lifetimes. Write only a number as your answer. Round to two decimal places (for example: 0.81).

Explanation / Answer

1) P(X>70.4)=1-P(X<70.4)=1-P(Z<(70.4-80.5)/9.9)=1-P(Z<-1.0202)=1-0.1538 =0.8462

2) for 57 percentile ; z=0.1764

hence corresponding score =mean =z*std deviation=43+0.1764*5=43.88

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