Question

2. An expensive watch is powered by a 3volt lithium battery expected to last years. Suppose the life of the battery has a standard deviation of year and is normally distributed. four 0.3 a. Determine the probability that the watch's battery will last longer than 4.8 years. b. Calculate the probability that the watch's battery will last more than 3.45 years. c. Compute the lengthoflife value for which 20 % of the watch's batteries last longer. a. The probability that the battery will last longer than 4.8 years is . (Round to four decimal places as needed.) b. The probability that the battery will last more than 3.45 years is . (Round to four decimal places as needed.) c. The lengthoflife value for which 20 % of the batteries last longer is years. (Round to one decimal place as needed.)

Kindly answer in excel sheet.

Answer 1

(I will be providing the EXCEL commands using which you will get the answers to your questions here.)
Here, X = battery lifetime ~ Normal(mean = 4, s.d. = 0.3).

(a) The probability that the battery will last longer than 4.8 years is = 0.0038.
EXCEL command: =1-NORMDIST(4.8,4,0.3,1).

(b) The probability that the battery will last more than 3.45 years is = 0.9666.
EXCEL command: =1-NORMDIST(3.45,4,0.3,1).

(c) The length of life value for which 20% of the batteries last longer is = 4.3 years.
EXCEL command: =NORMINV(0.8,4,0.3).