i am not sure where my mistake is . Can someone pls check for me .
Q : In a test , the math marks if candidates at a certain centre are normally distributed with a mean of 55 marks and a standard deviation of 5 marks . If a sample of 5 students is chosen at random , find the probability that at least one student obtains marks of less than 60 .
My working :
Let X be the random variable of the math marks of the candidates ..
X - N ( 55 , 25 )
P ( X < 60 ) = 0.84134
then , let Y be the random variable of the number of students obtaining marks less than 60 .
X - B ( 5 , 0.84134 )
therefore P ( Y ≥ 1 ) = 0.999 ----- my answer
But the answer given is 0.5784
Where did i go wrong ??