The random variable X is normally distributed with μ = 304.6 and σ = 13.2. If we know that X is larger than 292.4, find the probability that X is less than 313.8. State your answer rounded to 3 places of decimal.
The useful life of a battery is thought to be normally distributed with σ = 3.85 months and μ = 50.4 months. For how many months should the battery be guaranteed if the manufacturer wishes only 1.5% of batteries to be subject to replacement under guarantee? Enter your answer to one place of decimal. Months will be understood and should not be entered.