1. Let Z be a standard normal variable.Find the value ofzifzsatisfies P(Z <z) = 0.9525.
2. Suppose X is a normal random variable with = 40and = 20.Find P(X > 73.4).
3. Suppose X is a normal random variable with = 35and = 10.Find P(21.4 < X < 39.7).
4. Laboratory experiment shows that the life of the average butterfly is normally distributed with a mean of 18.8 days and a standard deviation of 2 days.Find the probability that a butterfly will live between 12.88 and 15.76 days.
5. Endure All, a manufacturer of batteries claims that the lifetime of their batteries is normally distributed with a mean of 500 hours and a standard deviation of 40 hours. What is the probability that an Endure All battery selected at random will last more than 550 hours?
6. Use the appropriate normal distribution to approximate the resulting binomial distributions.A fair coin is tossed 130 times.What is the probability of obtaining between 56 and 73 tails, inclusive?
7. Use the appropriate normal distribution to approximate the resulting binomial distributions.A convenience store owner claims that 55% of the people buying from her store, on a certain day of the week, buy coffee during their visit.A random sample of 35 customers is made.If the store owner's claim is correct, what is the probability that fewer than 23 customers in the sample buy coffee during their visit on that certain day of the week?