1) Determine the area under the standard normal curve that lies to the left of (a)Z=1.31 (b)Z=1.06 (c)Z=0.57 and (d)Z=0.14.2) Determine the area under the standard normal curve that lies to the right of (a)Z=0.64 (b)Z=-1.78 (c)Z=0.93 and (d)Z=0.593) Determine the area under the standard normal curve that lies between (a)Z=-0.64 and Z=0.64, (b)Z=-2.38 and Z=0, and (c) Z=-0.65 and Z=1.234) Find the Z-score such that the area under the standard normal curve to the right is 0.155) Find the z-scores that separate the middle 95% of the distribution from the area in the tails of the standard normal distribution.6) Find the value of zα α=0.187) Assume the random variable X is normally distributed with mean μ=50 and standard deviation σ=77 Find the 97th percentile.8) The mean incubation time for a type of fertilized egg kept at 100.33°F is 22 days. Suppose that the incubation times are approximately normally distributed with a standard deviation of 2 days.(a)What is the probability that a randomly selected fertilized egg hatches in less than 20 days?(b) What is the probability that a randomly selected fertilized egg takes over 24 days to hatch?(c) ) What is the probability that a randomly selected fertilized egg hatches between 18 and 22 days?(d) Would it be unusual for an egg to hatch in less than 19 days? Why?9) Suppose that the lifetimes of light bulbs are approximately normally distributed, with a mean of 56hours and a standard deviation of 3.3hours. With this information, answer the following questions.(a) What proportion of light bulbs will last more than 62hours?(b) What proportion of light bulbs will last 50 hours or less?(c) What proportion of light bulbs will last between 58 and 62 hours?(d) What is the probability that a randomly selected light bulb lasts less than 45 hours?10) The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with a mean of 1262 chips and a standard deviation of 118 chips. (a) Determine the 28th percentile for the number of chocolate chips in a bag.(b) Determine the number of chocolate chips in a bag that make up the middle 96% of bags.11) The time required for an automotive center to complete an oil change service on an automobile approximately follows a normal distribution, with a mean of 19 minutes and a standard deviation of 2.5 minutes.(a) The automotive center guarantees customers that the service will take no longer than 20minutes. If it does take longer, the customer will receive the service for half-price. What percent of customers receive the service for half-price?(b) If the automotive center does not want to give the discount to more than 5% of its customers, how long should it make the guaranteed time limit?

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