An image of a sales person making a cold call.

The success rate a salesman may achieve through cold calling will largely depend on the approach they take. According to Charlie Cook, author and marketing consultant, conversion rates for cold calls usually fall in the 2 percent range, while referrals may have a 50 percent conversion and solid leads may have a 20 percent conversion. A group of salesmen was assigned to pursue 100 "solid leads" during the period of a week.
  • Let X\displaystyle {X} be the number of sales generated from 100 "solid leads". Describe the distribution of X\displaystyle {X} and its parameters:

X∼\displaystyle {X}\sim  ( n=\displaystyle {n}= , p=\displaystyle {p}= )

  • Use the random variable notation to symbolically express the probability that at least 23 sales will be generated from 100 "solid leads":

  • Let Y\displaystyle {Y} be a normal variable that will be used to approximate the probability in question. Find the parameters of Y\displaystyle {Y} (round the answers to 2 decimal places):

 Y∼\displaystyle {Y}\sim ( μ=\displaystyle \mu= , σ=\displaystyle \sigma= )

  • Use the random variable notation to symbolically express the approximate probability that at least 23 sales will be generated from 100 "solid leads":

  • Use the correction for continuity:

  • Find the probability (round the answer to 4 decimal places):

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