The life span of television sets built by a particular manufacturer is normally distributed, with a mean of 10.2 years and a standard deviation of 1.7 years. The manufacturer will replace a television set if it breaks before the guarantee period is over.
a) If the manufacturer sets the length of the guarantee at 7 years, what proportion of the television sets will the manufacturer have to replace (Sentence)?
b) What is the maximum life span of the bottom 25% of television sets (Sentence)? What is the minimum life span of the top 25% of television sets (Sentence)? What name is given to the difference between these two values?
c) What is the maximum height of the normal distribution defined above? If you wanted to fit this normal distribution over the top of a histogram of a sample of 60 television sets with a class width of 2 years, what scaling factor would you use.