For the following examples, decide whether x is a binomial random variable.

a. You randomly select 3 bonds out of a possible 10 for an investment portfolio.

Unknown to you, 8 of the 10 will maintain their present value, and the other 2 will lose value due to a change in their ratings. Let x be the number of the 3 bonds you select that lose value.

b. Before marketing a new product on a large scale, many companies will conduct a consumer preference survey to determine whether the product is likely to be successful.

Suppose a company develops a new diet soda and then conducts a taste preference survey in which 100 randomly chosen consumers state their preferences among the new soda and the two leading sellers. Let x be the number of the 100 who choose the new brand over the two others.

c. Some surveys are conducted by using a method of sampling other than simple random sampling (defined in Chapter 3). For example, suppose a television cable company plans to conduct a survey to determine the fraction of households in the city that would use the cable television service. The sampling method is to choose a city block at random and then survey every household on that block. This sampling technique is called cluster sampling. Suppose 10 blocks are so sampled, producing a total of 124 household responses. Let x be the number of the 124 households that would use the television cable service.