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)

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%.

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frika frika · Answer 2 · 2018-08-26T07:58:14-04:00

frika frika

26-08-2018

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.

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