8 Probability Distributions

8.1 Binomial Distribution:

  1. Determine the Binomial distribution for which mean is 4 and variance is 3

  2. The incidence of disease due to Malnutrition is noticed in 20% of children in an area. What is the probability that out of 6 children selected at random (i) No child to get the disease (ii) One child to get the disease and (iii) 4 or more children will get the disease?

  3. If on average, rain falls on 12 days in every 30 days, find the probability that (1) Ist of 4 days even in a week will be fine and the remaining days as wet.

  4. The incidence of occupational disease in industry is such that the workers have 20% of chance of suffering from it. What is the probability that out of 6 workers 4 on more workers will have the chance of suffering from occupational disease?

8.1.1 Poisson Distribution:

  1. 10% of tools produced in certain manufacturing process turned out to be defective. Find the probability that in a sample of 10 tools chosen at random if the no of defective follows Poisson distribution a) exactly 2 will be defective b) At least 4 will be defective c) At most 4 will be defective

  2. A company known on the past experience that 3% of the bulbs they produced are defective. Assuming Poisson distribution find the probability of getting the following in a sample of 100 bulbs:

    1. No defective

    2. 1 defective

    3. 2 Defectives

    4. 3 defectives.

  3. It is noted that one tree out of 2000 trees of a farm used to get fire every year by lightning. If there are 4000 trees in a farm, what is the probability that exactly five trees will get fire during that year?

  4. A book contains 200 printing mistakes distributed randomly throughout its 200 pages. What is the probability that a page observed at random contain at least 2 printing mistakes?

3### Normal Distribution:

  1. Height of Barley plants in a field is assumed to follow normal distribution with an average height of 87.5 cm and with a S.D of 10 cm. A sample of 150 plants was selected from a plot of the field. Find the number of plants

(a) Having height between 70 cm and 90 cm

(b) Having height more than 100 cm.

(c) < 70 cm.

  1. Find the probability that a standard normal variate will lie between 0 and 1.25

  2. Given that the average height attained by certain tree species is 50m with standard deviation of 8m. Find the probability that the height of tree grown in a farm is in between 34 and 62ms.

  3. Given that the average number of rainy days in a place per year is normally distributed with mean number of days is 200 and standard deviation of 25 days. Find the probability that in a particular year there are more than 240 rainy days.

  4. It is known that the average duration of crop is 120 days with a standard deviation of 40 days. Assuming that the duration of crop is normally distributed. Find

    1. Probability that duration of crop exceeds 150 days

    2. Probability that the duration between 100 and 150 days

    3. Probability between 60 and 90 days.