Construct a 95% confidence interval for the true mean. A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8,000. A survey of owners of that tire design is conducted. Of the 32 tires surveyed, the mean lifespan was 46,400 miles with a standard deviation of 9,800 miles. Using alpha = 0.05, is the data highly consistent with the claim? Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your lower and upper bounds to the nearest whole number.)