S1 Normal Distribution Question

I'm pretty sure this topic is in the bad book in some of the A level Maths students because the questions can be sooooo random. (well for me at least )

anyways, im struggling to do this question, so I was wondering if you guys could help me

I got 0.6915 but thats wrong (but since there are 3 bicycles, i was going to multiply by 3 but thats still wrong), the answer is actually ?0.3307

The time taken in minutes, T, for a mechanic to service a bicycle follows a normal distribution with a mean of 25 minutes and a variance of 16 minutes
One afternoon the mechanic has 3 bicycles to service.
(c) Find the probability that he will take less than 23 minutes on each of the three bicycles.
(4 marks)

Have you drawn a diagram / mapped the standard dev / mean onto the standard normal distribution curve?

yeah, the mean is 25 and the S.D is 4 and i even did 1 minus as it asked for LESS than 23mins

yeah, the mean is 25 and the S.D is 4 and i even did 1 minus as it asked for LESS than 23mins

Why did you do that? You're not using an approximation requiring a continuity correction are you?

No no - convert it using z = \frac{x - mean}{standard deviation}

OH IM confused

Right, let's deal with this. You know that the mean is 25 and the Standard Deviation is 4 (square root of 16). So you need to find P(Z< (23-25)/4). What do you get for that?

-0.5

Yes, it's -0.5

But what's P(Z<-0.5)? That's the probability of Z being less than -0.5 on the standardised normal distribution.

Have you worked out the standard error? or used the standard deviation?

No no - convert it using z = \frac{x - mean}{standard deviation}

That's correct. So 1-0.6915 is 0.3085. This is the probability that he takes less than 23 minutes for 1 bike. Now what?

Is it not standarddeviation/ the root of n?

No, it isn't.

this is where im confused
i thought times by 3 but im not too sure

why..