Answer to Question #289711 in Statistics and Probability for Netu

Question

The average time it takes a group of Senior High School student to complete a certain examination is 48.2 minutes. The standard deviation is 7 minutes. Assume that the variable is normally distributed. If 20 randomly selected SHS student take the examination, what is the probability that the mean time it takes the group to complete the test will be more than 45 minutes?

Answer 1

$P(\bar x >45)=P(z>\frac{45-48.2}{\frac{7}{\sqrt{20}}})\\ =P(z>-2.04)=0.5+P(0<z<2.04)\\ =0.5+0.4793=0.9793$