Finding Probabilities using the Normal Distribution Problem 1. A national study found that college students with jobs worked an average of 22 hours per week. The standard deviation is 9 hours. A college student with a job is selected at random. Find the probability that the student works for less than 4 hours per week. Assume that the lengths of time college student's work are normally distributed and are represented by the variable X. (3 points) X - 0' Hint: Convert the normal distribution X to Standard normal using Z formula Z = and then look the Zvalues from the table and then nd the probability. Problem 2. The average speed of vehicles traveling on a stretch of highway is 67 miles per hour with a standard deviation of 3.5 miles per hour. Avehicle is selected at random. What is the probability that it is violating the speed limit of 70 miles per hour? Assume the speeds are normally distributed and are represented by the variable X. (3 points) 7\"\" 0' Hint: Convert the normal distribution X to Standard normal using Z formula Z = and then look the Z-values from the table and then nd the probability. Problem 3. A survey indicates that for each trip to a supermarket, a shopper spends an average of 43 minutes with a standard deviation of 12 minutes in the store. The lengths of time spent in the store are normally distributed and are represented by the variable X. A shopper enters the store. Find the probability that the shopper will be in the store for each interval of time listed below. 3a) Find the probability that the shopper will be in the store between 33 and 66 minutes. (3 points) X - u 6 Hint: Convert the normal distribution X to Standard normal using Z formula Z = and then look the Z-values from the table and then nd the probability. 3b) Find the probability that the shopper will be in the store for more than 39 minutes. (2 points) X - u 0' Hint: Convert the normal distribution X to Standard normal using Z formula Z = and then look the Z-values from the table and then nd the probability. Problem 4. What is the probability that the shopper in Example 3 will be in the supermarket between 31 and 58 minutes? (3 points) X-u 0' Hint: Convert the normal distribution X to Standard normal using Z formula Z = and then look the Z-values from the table and then nd the probability. Problem 5. Utility Bills The monthly utility bills in a city are normally distributed and represented by the variable X, with a mean of $100 and a standard deviation of $12. Find the probability that a randomly selected utility bill is (a) less than $70, (2 points) (b) between $90 and $120, (2 points) (0) more than $140. (2 points) X - u Hint: Convert the normal distribution X to Standard normal using Z formula Z = 0 and then look the Zvalues from the table and then find the probability