(b) A state-wide housing study found that 36% of adults in NSW have a mortgage. (i) A random sample of 25 adults in NSW is to be taken to determine the proportion of 2 those who have a mortgage. Show that the mean and standard deviation for the distribution of sample proportions of such random samples are 0.36 and 0.096 respectively. (ii) Part of a table of P(Z S z) values, where Z is a standard normal variable, is shown. 2 2 +0.00 +0.01 +0.02 +0.03 +0.04 +0.05 +0.06 +0.07 +0.08 +0.09 2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 Of a random sample of 25 adults in NSW, use the table to estimate the probability that at most three will have a mortgage. Give your answer correct to four decimal places