Normal Distribution revision questions

1. An experiment consists of drawing a disk from a bag containing 5 disks labelled A, B, C, D or E and then replacing it. What is the probability that A will not be chosen?

The bag is then thoroughly shaken before another draw is made. Calculate the approximate probability of obtaining disc A at least

a) 2050 times when the experiment is performed 10000 times

b) 180 but not more than 190 times when the experiment is performed 900 times.

2. The probability that a child is left handed is 0.16.

Calculate the mean and standard deviation of the number of left handed children in a random sample of 100 children.

Taking the distribution of left handed children in the sample as approximately normal, calculate the probability that a random sample of 100 children contains fewer than 24 left handed children.

3. The marks of 200 candidates in an exam are normally distributed with mean 52 and standard deviation 18.

If the pass mark is 47 calculate the percentage of candidates who failed.

10% of the candidates are awarded a distinction. Find the mark necessary to gain a distinction.

4. If the random variable X has a probability density function N(0,2) find

a) P(X<=1.2)

a) P(-1<=X<=1.2)