02 May 1. The vice president of Offshore Oil & Gas, a consulting firm, notices that the average length of time that a consultant spends on the telephone with a client at any one time is 40 minutes with a standard deviation of 18 minutes. Assuming that the length of such conversations is normally distributed, what percent of the consultants’ phone calls would take longer than 50 minutes? 2. The rate at which a swimming pool is filled is uniformly distributed between 20 and 26.3 gallons per minute. a) What is the probability that the filling rate at any one time is between 21.3 and 24.6 gallons per minute? b) What is the mean rate at which the swimming pool is filled? c) What is the standard deviation of the rate at which the swimming pool is filled? 3. Yellow Rise Taxi Company estimates that it makes an average of $415 in profits per day. Assuming that the daily profit follows an exponential distribution, what is the probability that on a given day at least $500 in profits will be made?
The posted speed limit on Interstate 70 is 70 miles per hour, but it is claimed that the mean of the actual speeds of vehicles is greater than 70 miles per hour. To test this claim, the speeds of 36 randomly selected vehicles were taken and reported to the right.
Speed of Randomly Selected Vehicles on I-70 68 77 65 71 77 73 62 78 68 72 77 72 74 72 74 70 76 72 73 71 75 70 70 74 75 61 74 72 69 75 84 79 83 75 71 76
(a) Give the null and alternative hypotheses for this situation in mathematical notation.
(b) Based upon a 10% level of significance, determine the critical value(s) associated with this hypothesis test.
(c) Determine the sample’s test statistic.
(d) State a final conclusion regarding the results of the hypothesis test. Make sure your statement is tied to the context of the problem (speed of vehicles on I-70).
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