A company makes batteries with an average life span of 300hours with a standard deviation of 75 hours. Assuming thedistribution is approximated by a normal curve fine theprobability that the battery will last:(give 4 decimal places foreach answer)a. Less than 250 hoursb. Between 225 and 375 hoursc. More than 400 hours

Answer:a) 0.2514b) 0.6827c) 0.0918Step-by-step explanation:Average life span of batteries = u = 300 hoursStandard deviation = s = 75 hoursGiven that the distribution of life span of batteries is normally distributed, so we can use z-score to find the said probabilities.Part a) Less than 250 hoursIn order to find the probability that the life span of battery will be less than 250 hours we need to convert x = 250 into z-score and then use z-score to find the probability from the z-table.The formula for z-score is:[tex]z=\frac{x-u}{s}[/tex]Using the values, we get:[tex]z=\frac{250-300}{75}=-0.67[/tex]From the z-table or z-calculator the probability of z-score being less than - 0.67 comes out to be 0.2514P(z < -0.67) = 0.2514Thus, the  the probability that the life span of battery will be less than 250 hours is 0.2514Part b) Between 225 and 375 hoursIn order to find the probability that the life span of battery will be between 225 and 375 hours we need to convert them into into z-scores and then use z-score to find the probability from the z-table.225 into z-score will be:[tex]z=\frac{225-300}{75}=-1[/tex]375 into z-score will be:[tex]z=\frac{375-300}{75}=1[/tex]Thus, from the z-table we now need to find that probability of z-score being in between -1 and 1. From the z-table this value comes out to be:P(-1 < z < 1 ) = 0.6827Thus, the probability that the life span of battery will be between 225 and 375 hours is 0.6827Part c) More than 400 hoursIn order to find the probability that the life span of battery will be more than 400 hours we need to convert x = 400 into z-score and then use z-score to find the probability from the z-table.The formula for z-score is:[tex]z=\frac{x-u}{s}[/tex]Using the values, we get:[tex]z=\frac{400-300}{75}=1.33[/tex]From the z-table the probability of z score being more than 1.33 comes out to be:P( z > 1.33) = 0.0918Thus, the probability that the life span of battery will be more than 400 hours is 0.0918