The table below shows the probability distribution function of the number of accidents (X) occur in a day by taxis belonging to a taxi company. x 0 1 2 3 4 P(X = x) 0.5 0.15 0.05 2k k (a) Find the value of k. (b) Find the expected value and standard deviation of the number of a

The probability that you will receive a wrong number call this week is 0.2. The probability that you will receive a sales call this week is 0.5. The probability that you will receive a survey call this week is 0.3. What is the probability that you will receive one of each this week? Express your answer up to 2 decimal places.(Assume independence.)

Assume the amount of time (in minutes)a postal clerk spends with his or her customer. The time is known to have an exponential distribution with the average amount of time equal to 10minutes.(a) What is the mean and standard deviation of the amount of time a postal clerk spends with his or her customer? (b) What is the probability that postal clerk spends with his or her customerlessthan 10 minutes?

The lifespans of light bulbs are known to follow an exponential distribution. The exponential distribution, often denoted exp(β), is characterized by a single mean parameter β. The exponential distribution has a unique property that its standard deviation is equal to its mean. Suppose you order 100 light bulbs known to each have lifespans (in years) distributed according to exp(4). What is the probability that the average lifespan of your 100 light bulbs exceeds 5 years? (Using R it possible)

IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X=X= IQ of an individual.   (f) The middle 50% of IQs fall between what two values?   (g) Sketch the graph and write the probability statement.

The Gompertz distribution is commonly used by biologists who believe that an exponential hazard rate should occur in nature. Suppose that the time to death in months for a mouse exposed to a high dose of radiation follows a Gompertz distribution with 0 = 0.01 and a = 0.25. Find (a) the probability that a randomly chosen mouse will live at least one year, (b) the probability that a randomly chosen mouse will die within the first six months, and (c) the median time to death.

The lifetime of a certain electronic component used in a laptop computer can be modeled by an exponential distribution with a mean of 4 years, or ux B = 4 years. = (a) Compute the standard deviation of the above distribution. SD(X) = 0x = years (use two decimals in your answer) (b) What can you say about the shape of the distribution of X? The distribution of X is ? (c) You randomly pick a laptop. Find the probability that the certain electronic component will last between 1 years and 4 years. P(1 ≤ X ≤ 4) = = (Use four decimals in your answer) (d) If the electronic component in the laptop you chose in (c) has lasted at least 4 years, what is the probability it will last in total at most 8 years? (Use four decimals in your answer) (e) The manufacturer of this electronic component wishes to have a guarantee. This guarantee will state that 3% of components will be replaced free of charge. At what lifetime should the manufacturer set the guarantee, in years? years (Use two decimals in…

Suppose we are waiting at the bus stop and a bus arrives every 30 minutes, on average. Let X represent your waiting time in minutes until the next bus arrives. X follows the exponential distribution. What is the probability that no bus arrives in the next 20 minutes, i.e. what is the probability of waiting more than 20 minutes for a bus P(X > 20)(a) 0.513(b) 0.487(c) 0.662(d) 0.958(e) Cannot be determined from the information given