Math Help - probability

1. probability

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 ??

2. Originally Posted by mathaddict
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 ??
Your working is excellent. Your answer is correct.

The given answer of 0.5784 is wrong. It's the probability that at least one student obtains marks of greater than 60.