Question

which of the following probabilities is the greatest for a standard normal distribution? a. p(-1.5≤z≤-0.5) b. p(-0.5≤z≤0.5) c. p(0.5≤z≤1.5) d. p(1.5≤z≤2.5)

Answer 1

All intervals are 1 unit long. You just have to look at the picture of normal distribution ( look at the attachment) and look which interval covers the most area.

You will see that p(-0.5<z<0.5) is the one that covers 34% of area, meaning the probability is 34%. All the other intervals are much less than 34%.

Answer 2

Look at the attached diagram. From this diagram you can conclude that:

1. $Pr(-1.5\le z\le -0.5)=0.092+0.15=0.242$ or 9.2%+15%=24.2%;

2. $Pr(-0.5\le z\le 0.5)=0.191+0.191=0.382$ or 19.1%+19.1%=38.2%;

3. $Pr(0.5\le z\le 1.5)=0.15+0.092=0.242$ or 15%+9.2%=24.2%;

4. $Pr(1.5\le z\le 2.5)=0.044+0.017=0.061$ or 4.4%+1.7%=6.1%.

As you can see the greatest value is $Pr(-0.5\le z\le 0.5)=0.382$ (19.1%+19.1%=38.2%).

Answer: correct choice is B.