The marketing division of the company wants to conduct a survey to gather information on customer satisfaction for the toothpaste, smile. The data on customer rating is obtained on a 3 point start rating, *** (3-star), ** (2-star), and * (one-star). Moreover, data on their age group L (

a) What is the probability that a respondent given 2-star (**) rating will belong to age group L?

b) What proportion of the respondents would rate the product 3-star (***)?

c) How likely a 40 years old respondent will rate the product one-star (*)?

d) Suppose a random variable is defined on the basis of the above data as number of respondents given 2-star (**) rating to the product. Develop a probability model for the random variable and find out its mean and variance.

e) Using the probability model, calculate the probability that at least three customers will be rating the product 2-star (**)?

The Survey is conducted in a shopping mall where the interviewer is standing at the entrance and record the number of footfalls per minutes. After conducting such an interview for three months, the interviewer finds that the data follows Poisson distribution with mean 2 per minute.

f) Define the relevant random variable which follows Poisson distribution. What is the mean and standard deviation of the distribution?

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g) Find the probability the number of footfalls on a weekday between 11:30-11:31 am will be 4.

h) Find the probability that at least 2 footfalls will be recorded between 7:00-7:05 pm.