Answer to Question #323308 in Statistics and Probability for Ali De Austria

Question

Because of the immediate suspension of classes nationwide due to the COVID-19 pandemic, many

schools opted to give the final examination online. The scores on a certain exam are normally

distributed with a mean of 75 and a standard deviation of 10. Find the probability of the score.

a. Less than 54

b. At least 50

c. The average age of the ABS CBN employees is known to be 32 years and the standard

deviation is 5 years. Find the probability that a random sample of 36 employees will have an average

age of less than 30 years.

Answer 1

X~$N(75,10^2)$

a) $P(X<54)=P(N(75,10^2)<54)=P(75+10N(0,1)<54)=P(N(0,1)<-2.1)=0.01786$

b) $P(X>50)=P(75+10N(0,1)>50)=P(N(0,1)>-2.5)=P(N(0,1)<2.5)=0.99379$

с) Y~$N(32, ({\frac {5} {\sqrt {36}}})^2)$

$P(Y<30)=P(N(32, ({\frac 5 {\sqrt {36}}})^2)<30)=P(32+{\frac 5 6}N(0,1)<30)=P(N(0,1)<-2.4)=0.00820$