In an examination the probability distribution of scores (X) can be approximated

Question

In an examination the probability distribution of scores (X) can be approximated by normal distribution with mean 70 and standard deviation 7.6. Suppose one has to obtain at least 55 to pass the exam. What is the probability that a randomly selected student passed the exam? [Answer to 3 decimal places] Submit Answer Tries 0/5 Ifr two students are selected randomly what is the chance that both the students failed? [Answer to 3 decimal places] Submit Answor Tries 0/5 If only top 9% students are given an award, then what was the minimum marks required to get the award? [Answer to 1 decimal place] Submit Answer Tries o/s

Explanation / Answer

1)P(X>55)=P(Z>(55-70)/7.6)=P(Z>-1.97)=0.976

2)P(both failed)=(1-0.976)*(1-0.976)=0.001

3)

for top 9 percent critical z =1.34

hence corresponding value =mean+z*std deviation=70+1.34*7.6 =80.2

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