Year 12s: what will be the first way you research your future options? >>

S2 distributions

The random variable H has the distribution B(n, p). It is given that, using a normal approximation, P(H ≥ 71) = 0.0401 and P(H ≤ 46) = 0.0122. Find the mean and standard deviation of the approximating normal distribution.

How do I tell in a question like this whether I need a continuity correction or not? It says that the two probabilities are found using the approximated normal distribution but how do we tell whether we are looking at H ≥ 71 on the normal distribution or H ≥ 70.5 (and analogous for the other - is it H ≤ 46 or H ≤ 46.5, and how should I tell)?

Reply 1

CTArsenal

I think the big clue is that they've said H~B(n,p), so the inequality hasn't been converted using the continuity correction :tongue:

P(X > 70.5) = 0.0401,
P(X < 46.5) = 0.0122,

where X~N(μ,σ²) :smile:

Reply 2

Big-Daddy

Original post by CTArsenal

I think the big clue is that they've said H~B(n,p), so the inequality hasn't been converted using the continuity correction :tongue:

P(X > 70.5) = 0.0401,
P(X < 46.5) = 0.0122,

where X~N(μ,σ²) :smile:

Thanks

so if they had wanted to refer to the approximate distribution instead of the exact, they'd have renamed the variable you think? (e.g. to X as you have done)

Reply 3

CTArsenal

Original post by Big-Daddy

Thanks

so if they had wanted to refer to the approximate distribution instead of the exact, they'd have renamed the variable you think? (e.g. to X as you have done)