2. A company has three machines B1, B2, and B3 for making 1 k2 resistors. It has been observed that 80% of resistors produced by B1 are within 50 N of the nominal value. Machine B2 produces 90% of resistors within 50 Q of the nominal value. The percentage for machine B3 is 60%. Each hour, machine B1 produces 3000 resistors, B2 produces 4000 resistors, and B3 produces 3000 resistors. All of the resistors are mixed together at random in one bin and packed for shipment. What is the probability that the company ships a resistor that is within 50 N of the nominal value?

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?

8.      Suppose that a bacteria population doubles every eleven hours.  If the initial population is 2,000 individuals, approximately how many hours would it take the population to reach 20,000?

Suppose that a commercial bakery produces chocolate chip cookies. Based on extensive testing, the bakery has determined that the ideal number of chocolate chips per cookie is 18. In the past, master bakers mixed the dough and spooned it onto sheet pans by hand, but the owners have decided to test a new machine. The machine extrudes dough onto baking sheets at a uniform rate. It runs continuously from 4:30 a.m. until 12:30 p.m. The number of chips per cookie depends on the viscosity of the dough, and because the dough stiffens as it sits in the machine, the machine produces cookies that contain the optimal number of chips, 18 per cookie, between the hours of 5:00 a.m. and 11 a.m. The distribution of cookies is shown in the graph below. The shaded area represents the proportion of all cookies that contain exactly 18 chocolate chips. 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 1:00 Compute the proportion of cookies produced each day that contain the optimal number of chocolate chips.…