The rate at which telephone calls are received by a single switchboard between 2pm and 4pm on a Friday afternoon is 7 an hour. Records are kept of the numbers of calls received in the 30-minute periods between 2.00 pm and 2.30 pm each Friday. What is the probability that, in four consecutive weeks, there are exactly three weeks in which at most one call is received during this time period? [First find P(at most one call received in 30 mins).]
could someone please explain the poisson dist. clearly!! thanx!
could someone please explain the poisson dist. clearly!! thanx!
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the poisson distribution has the formula P[x] = e^-m *m^x/x!
here m = 7 per hour, but here we are concerned with half-hour periods. in such situations, we change m proportionately, so m = 3.5
P[≤1] = P[0] + P[1] = e^-3.5*3.5^0/0! + e^-3.5*3.5^1/1! = 0.1359 to 4 dp
this is the Pr for any ONE half-hour period. to get the desired answer, we now use the familiar binomial distribution with n = 4, p = 0.1359 to get
P[3] = 4c3*0.1359^3*0.8641 = 0.0087 <-------
here m = 7 per hour, but here we are concerned with half-hour periods. in such situations, we change m proportionately, so m = 3.5
P[≤1] = P[0] + P[1] = e^-3.5*3.5^0/0! + e^-3.5*3.5^1/1! = 0.1359 to 4 dp
this is the Pr for any ONE half-hour period. to get the desired answer, we now use the familiar binomial distribution with n = 4, p = 0.1359 to get
P[3] = 4c3*0.1359^3*0.8641 = 0.0087 <-------