Question

1. a test consists of 25 multiple choice questions with 5 possible answers, only 1 of which is correct. find the mean and standard deviation. ( binomial)

2. Duchess county , N.Y, has been experiencing a mean of 35.4 motor vehicle deaths each year.

a. find the mean number of deaths per day. (poisson)

b. find the probability that on a given day, there are more than 2 motor vehicle deaths

Answer 1

(1) Probability of correct answer = 1/(number of possible answers) =1/5 = 0.2

Number of questions (n) = 25

Mean = n*p = 25*0.2 = 5

Standard deviation =

=

=

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(2) Given that the mean is 35.4 motor vehicle deaths each year.

(a) mean number of deaths per day = (mean number of deaths per year)/(number of days in a year)

= 35.4/365

= 0.097 (3 decimals)

(b) We have to find P(X more than 2 motor vehicle deaths)

Using formula