fter your complaint about their service, a representative of an insurancecompany promised to call you "between 7 and 9 this evening." Assumethat this means that the time T of the call is uniformly distributed in thespecied interval.(a) Compute the probability that the call arrives between 8:00 and 8:20.(b) At 8:30, the call still hasn't arrived. What is the probability that itarrives in the next 10 minutes?(c) Assume that you know in advance that the call will last exactly 1hour. From 9 to 9:30, there is a game show on TV that you wantedto watch. Let M be the amount of time of the show that you missbecause of the call. Compute the expected value of M .

Calls arrive at a call center at the rate of 42 per hour.What is the probability that the next call arrives in a.less than 2 minutes? b.more than 4 minutes? c.less than 1 minute? Round to four decimal places as​ needed.

Q20.  If calls arrive at a telephone exchange such that the time of arrival of any call is independent of the time of arrival of earlier of future calls, the probability distribution function of the total number of calls in a fixed time interval will be*NormalBinomial distributionPoisson distributionNone of thes

Question 7A statistical analysis of 2,000 long-distance telephone calls made from the headquarters of theBricks and Clicks Computer Corporation indicates that the length of these calls is normallydistributed, with 𝜇 = 300 seconds and 𝜎 = 50 seconds. (4 marks)(a) What is the probability that a call lasted less than 210 seconds?(b) What is the probability that a call lasted between 210 and 320 seconds?(c) What is the probability that a call lasted between 100 and 210 seconds?(d) 10% of all calls will last less than how many seconds?

Shuttle bus which links the Clayton campus to the Caulfied campus starts operating at 5:00 am and will have a service every half hour. Suppose that none of the seats on the bus are completely occupied and that there is always some room for passengers. A student who wants to travel to Caulfied arrives at the bus stop at a (uniform) random time between 8:45 am and 9:45 am. What is the probability that he/she waits at most 10 minutes? Write down your answer to an accuracy of 2 decimal points.

Riya leaves for school between 7:00 AM and 7:15 AM. She takes between 20 and 30 minutes to reach the school. Let 𝑋X denote her time of departure, and let 𝑌Y denote her travel time. Assuming that 𝑋X and 𝑌Y are continuous, independent and uniformly distributed, find the probability that she reaches the school before 7:30 AM. Enter the answer correct to two decimal places.