Why using the normal distribution as an approximation to the binomial distribution ?
For large numbers of trials, calculating the binomial distribution can be difficult (e.g. )
The normal approximation eliminates all errors in probability estimates for binomial variables
Binomial distributions are only defined for small sample sizes, so the normal distribution is needed for large n
As n (number of trails) becomes large, if the probability is close to 0.5, the distribution tends towards a normal distribution.
In A Level S1 Course, we say that the normal distribution is a good approximation for the binomial distribution if
np>5 and n(1-p)>5.
np>10 and n(1-p)>10.
np>15 and n(1-p)>15.
np>5 and n(1-p)>10.
Normal distribution is continuous and Bin. distribution is discrete, we need to make a small adjustment when doing our approximation. This adjustment is called
Continuity correction
Error correction
B(30, 0.95) can be well-approximated by a normal distribution
Binomial distributions B(20, 0.6) can be well-approximated by a normal distribution.
Find the smallest possible value of n for B(n, 0.024) can be well-approximated by a normal distribution. n=______.
The discrete random variable Y ~ B(50, 0.6). Use a suitable approximation and continuity correction to find P(Y > 26)=_________ .(3 sf)
X ~ B(100, 0.7),P(X < 75)=_____.
Y ~ B(50, 0.6). Use a suitable approximation and continuity correction to find P(Y > 26)=_______. 3sf
C~B(40,0.25). _______.3sf
D~B(400,0.02), ______. 3sf
A fair coin is tossed 400 times. Given that it shows a head on more than 205 occasions, find an approximate value for P(a head on fewer than 215 occasions)=___
You should understand the question before jumping to next questions !
An ordinary fair die is rolled 450 times. Given a 6 is rolled on fewer than 80 occasions, find approximately P(a 6 is rolled on at least 70 occasions)=___3sf
An ordinary fair die is rolled 450 times. Given a 6 is rolled on fewer than 80 occasions, find approximately P(a 6 is rolled on at least 70 occasions)=___3sf