Calculate the expected number of unsuccessful attempts

Reference no: EM132650806

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

Questions Cloud

Terrorist profiles and group dynamics : Select two different terrorist organizations. Compare and contrast the profiles of these groups. How do their motivations differ? How are they similar?

Discuss what activity-based costing is : Discuss what activity-based costing is and examine how it impacts the role of management accountants in the broader context of performance management

Attack justification-justification for terrorism : Discuss the role of religion in the justification for terrorism. Identify a terrorist organization which you feel is rooted in religious ideology

On what amount is the Federal gift tax computed : Elizabeth made taxable gifts of $3 million in 2019 and $14 million in 2020. On what amount is the Federal gift tax computed for the 2020 gift

Calculate the expected number of unsuccessful attempts : Calculate the expected number of unsuccessful attempts made by Stephanie on any day that she tries to log in and Calculate variance.of X.

Discuss the Federal estate tax consequences of these deaths : Within a period of two years and on different dates, all three sisters die. Discuss the Federal estate tax consequences of these deaths

Which are features of a just-in-time manufacturing system : Which are features of a just-in-time manufacturing system? Less wasted movement of material and people. / Centralized maintenance areas

Compute the present value of the transfer tax : Felipe's after-tax rate of return on his real estate investments is 3%. Compute the present value of the transfer tax

How the new process accounting approach affect : How the new process accounting approach affect each business unit's incentives and tools to control costs. Explain what Boeing means by process accounting.

User Account

All Pages