It has been argued that although there may be more claims when road conditions are slippery in the winter, this should not affect the average claim. Malpeque took a sample of 50 claims from the winter of 2018 and found that the average claim was $1,742. Although this seemed somewhat higher than average, Malpeque was familiar with the wide variation in claims and was prepared to accept that the average was similar to the summer.
What is the probability that the sample average would be as high, or higher, than $1,742 if the true average of all claims was $1,500? Assume that the standard deviation remains $500. What do you think about the belief that the average is unaffected?