Even more Normal Distribution revision questions

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1. In a large batch of free range eggs 38% were less than 30g in weight.

12% were over 40g in weight.

Assuming that the distribution of eggs is Normal find the mean and standard deviation of the eggs.

If there were 2000 eggs estimate how many were between 36g and 42g in weight.

2. In a series of eight matches between two cricket teams, calculate the probability that one team wins the toss,

a) On exactly 5 occasions,

b) On more than 5 occasions.

3. In a multiple-choice test there are four alternatives for each question. Only one alternative is the correct answer. The test has 30 questions. A student guesses every answer. If the pass mark is 20, calculate the probability that the student passes.

4. If the random variable X has a probability density function N(5, 4), find:

a) P(X<=5.2)

b) P( 5.2<=X<=5.6)

5. The time taken for Lakes School pupils to travel from home to school is known to be Normally distributed with a mean of 35 minutes and a variance of 20 minutes.

a) Calculate the probability that a pupil, chosen at random, takes more than 40 minutes to get to school.

b) If there are 840 pupils at the school, how many of them take between 30 and 40 minutes to travel to school?

5. If X~N(5, 25)

a) Find P(4<=X<=6)

b) Find the percentage of values that lie between 1 and 10

6. In a test there are 600 candidates, whose results are Normally distributed with a men of 70 and a standard deviation 25.

If 550 candidates pass the exam, find the pass mark.