Please use R programming to answer this question:

1. A certain type of storage battery lasts, on average 3 years with a standard deviation of 0.5 year.

Assume that battery life has a normal distribution.

a. find the probability that a given battery will last less than 2.3 years.

b. Refer to part (a). Give a graph of the probability density that corresponds to this distribution. Shade

the region that corresponds to the probability, and add the probability to the graph.

c. Find the 90th percentile of the distribution battery life.

d. Give the graph of the cumulative distribution, and add line segments to identify the 90th percentile

on the plot.