In writing please, and step by step.

Read Sections 7.1, 7.2, and 7.3 from the book before you start. You can use the tables in the back of your book or your calculator. Show all your steps. 1. The mean blade length of a rapier, which is a fencing sword, is 90.0 cm with a standard deviation of 4.2 cm. If 38 rapiers are randomly sampled, what is the probability that their mean blade length is less than 88 cm? 2. One brand of light bulbs has a mean lifetime of 400 hours with a standard deviation of 28 hours. What is the probability that the lifetime of one randomly chosen bulb will differ from the mean by over 50 hours? Assume that the population is normally distributed. 3. At one theater, moviegoers spend a mean of $6.32 on refreshments with a standard deviation of $2.55. What is the probability that the mean amount spent on refreshments by a random sample of 50 moviegoers will be between $6 and $7