According to a government study among adults in the 25 to 34

According to a government study among adults in the 25- to 34-year age group, the mean amount spent per year on reading and entertainment is $1,999. Assume that the distribution of the amounts spent follows the normal distribution with a standard deviation of $574. (Round z-score computation to 2 decimal places and your final answer to 2 decimal places. Omit the \"%\" sign in your response.)

Solution

1. p(x) > 2500 = p[z > (2500-1994) / 450)] = p(z) > 1.1244 = 0.1304; 13.04 percent

2. p(2500 <= x <= 3000); 1.1244 <= p(z) <= (3000-1994) / 450; 1.1244 <= p(z) <= 2.2355 = 0.1177; 11.77 percent.

3. p(z) < 1000 = p(z) < (1000-1994) / 450); p(z) < -2.2088 = 0.0136; 1.36 percent