The life of a certain brand of battery is normally distributed, with mean 128 hours and standard deviation 16 hours. what is the probability that a battery you buy lasts at most 100 hours? standardize the variable. x = 100 is equivalent to z =

Answer with Step-by-step explanation:The life of a certain brand of battery is normally distributed, with mean 128 hours and standard deviation 16 hours. Let X be the life time of a battery.when, X=100the formula for z is:z=X-mean/standard deviationz= 100-128/16z= -28/16z=-1.75P(X≤100)=P(z≤-1.75)             = P(z≥1.75)            =0.0409   (using z-dist table)Hence,  probability that a battery you buy lasts at most 100 hours is:0.0409