At a police station in a large city, calls come in at an average rate of four calls per minute. Assume that the time that elapses from one call to the next has the exponential distribution. Take note that we are concerned only with the rate at which calls come in, and we are ignoring the time spent on the phone. We must also assume that the times spent between calls are independent. This means that a particularly long delay between two calls does not mean that there will be a shorter waiting period for the next call. We may then deduce that the total number of calls received during a time period has the Poisson distribution. a. Find the average time between two successive calls. b. Find the probability that after a call is received, the next call occurs in less than ten seconds.

Researchers have created every possible "knockout" line in yeast. Each line has exactly one gene deleted and all the other genes present (Steinmetz et al. 2002). The growth rate—how fast the number of cells increases per hour—of each of these yeast lines has also been measured, expressed as a multiple of the growth rate of the wild type that has all the genes present. In other words, a growth rate greater than 11 means that a given knockout line grows faster than the wild type, whereas a growth rate less than 11 means it grows more slowly. The growth rate of a random sample of knockout lines is 0.86, 1.02, 1.02, 1.01, 1.02, 1, 0.99, 1.01, 0.91, 0.83, 1.01 What is the standard deviation and variance of growth rate for this sample?

If a city's population is 1.3 million now and will grow at a continuous rate of 4.5% in the future, what will the city's population be in the year 2030? Give your answer in millions of people with two places of accuracy to the right of the decimal.

Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model. A sample of  2100  bacteria selected from this population reached the size of  2335  bacteria in three hours. Find the hourly growth rate parameter. Note: This is a continuous exponential growth model.   Write your answer as a percentage. Do not round any intermediate computations, and round your percentage to the nearest hundredth.