00:01
Hello students, we have given the parameters of binomial distribution that is n is equal to 40 and probability p is equal to 0 .55.
00:12
Now by using this we have to first compute the mean and standard deviation.
00:17
Now we know the formula for mean of binomial distribution is equal to np which is equal to 40 into 0 .55 is equal to 22.
00:30
So this is the mean.
00:32
Then standard deviation is equal to square root of np into 1 minus p which is equal to, so after putting all the values here we will get the standard deviation is equal to 3 .1462.
00:48
Then in the b part we have to calculate the probability that x is greater than or equal to 25.
00:55
Now here by applying correction factor, by applying correction factor, probability of x greater than or equal to 25 is nothing but probability of x greater than or equal to 24 .5.
01:20
Now here by using the normal approximation we can write this probability as probability of x minus mean divided by standard deviation is greater than or equal to 24 .5 minus mean is 22 divided by standard deviation is 3 .1462.
01:42
So therefore this is equal to probability of, now this is nothing but the standard normal variable that is z is greater than or equal to 0 .79 and by using the z table we will get this probability as 0 .2147.
02:00
So therefore probability of x greater than or equal to 25 is 0 .2147.
02:06
Then in the c part we have to calculate probability of x less than or equal to 15.
02:12
Now here also by using the correction factor this probability is nothing but probability of x less than or equal to 15 .5.
02:22
So therefore this is equal to the probability in terms of z is probability of z less than or equal to minus 2 .06 and this probability is 0 .0197...