Question

Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1.

If P(−b<z<b)=0.3278P(-b<z<b)=0.3278, find b.

b=  (Round to three decimal places.)

Hint: Consider symmetry on this problem and draw a picture of the normal distribution to visualize this problem.

• What is the area under the normal curve from 0 to b?
• What is the area under the normal curve from −∞-∞ to 0?
• Given that information, what is the area under the normal curve from −∞-∞ to b?
• Given that information, what calculator function can you use to find b?

Answer 1

Now,

and similarly,

So, we can write,

So,

(ans)

The area under the normal curve from 0 to b =

The area under the normal curve from −∞ to 0

The  area under the normal curve from −∞ to b

I have used minitab software -> calc -> probability distribution -> normal