Calculate the expected number of unsuccessful attempts

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Question 1
A list of all possible values of the discrete random variable X, together with their associated probabilities, is called a probability distribution. It is often helpful to show the probability distribution in a table.
Stephanie is very forgetful. Every time she logs in to her online bank she only has a 40% chance of remembering her password correctly. She is allowed 3 unsuccessful attempts on any one day and then the bank will not let her try again until the next day.

(a) Draw a fully labelled tree diagram to illustrate this situation.
(b) Let X be the number of unsuccessful attempts Stephanie makes on any day that she tries to log in to her bank. Construct a table to show the probability distribution of X.
(c) Calculate the expected number of unsuccessful attempts made by Stephanie on any day that she tries to log in.
(d) Calculate variance.of X.

Question 2

Eight friends take a picnic to a cricket match. As her contribution to the picnic, Manisha buys eight sandwiches at a supermarket. She selects the sandwiches at random from those on display. The probability that a sandwich is suitable for vegetarians is independently 0.3 for each sandwich. Consider a Binomial distribution.

(a) Find the probability that, of the eight sandwiches, the number suitable for vegetarians is:
(i) 2 or fewer ;

(ii) exactly 2 ;

(iii) more than 3.

(b) The weights, in kilograms, of men and women have the distributions N(78, 72) and N(66, 52) respectively.

(i) State two theorems of Expectation and two theorems of Variance.
(ii) The maximum load that a certain cable car can carry safely is 1200 kg. If 9 randomly chosen men and 7 randomly chosen women enter the cable car, find the probability that the cable car can operate safely.

(iii) Find the probability that a randomly chosen woman weighs more than a randomly chosen man.

Reference no: EM132650806

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