Suppose, household color TVs are replaced at an average age of I4 = 7.4 years after purchase, and the (95% of data) range was from 3.6 to 11.2 years. Thus, the range was 11.2 3.6 = 7.6 years. Let x be the age (in years) at which a color TV is replaced. Assume that X has a distribution that is approximately normal. I USE SA (a) The empirical rule indicates that for a symmetric and bell-shaped distribution, approximately 95% of the data lies within two standard deviations of the mean. Therefore, a 95% range of data values extending from y 20 to y + 20 is often used for "commonly occurring" data values. Note that the interval from )4 20 to ll + 20 is 46 in length. This leads to a "rule of thumb" for estimating the standard deviation from a 95% range of data values. Estimating the standard deviation For a symmetric, bell-shaped distribution, range ~ high value low value " 4 standard deviation :2 where it is estimated that about 95% of the commonly occurring data values fall into this range. Use this "rule of thumb" to approximate the standard deviation ofx values, where x is the age (in years) at which a color TV is replaced. (Round your answer to one decimal place.) 1.9 yrs (b) What is the probability that someone will keep a color TV more than 5 years before replacement? (Round your answer to four decimal places.) -1.3 x (c) What is the probability that someone will keep a color TV fewer than 10 years before replacement? (Round your answer to four decimal places.) (d) Assume that the average life of a color TV is 7.4 years with a standard deviation of 1.9 years before it breaks. Suppose that a company guarantees color TVs and will replace a TV that breaks while under guarantee with a new one. However, the company does not want to replace more than 15% of the TVs under guarantee. For how long should the guarantee be made (rounded to the nearest tenth of a year)? yrs