Suppose the National Real Estate Association for a particular state would like to test the hypothesis that the average number of days a home is on the market during 2018 was 60 days. To test this hypothesis, 32 homes sold during 2018 were selected and the number of days the homes were on the market was recorded. Assume the (population) standard deviation for the time on the market is 25 days.

Using a 5% level of significance, calculate the probability of a Type II error occurring if the actual average time for a house on the market is 57 days. Show all the necessary steps to answer the question.