Question

answer the following.
(a) the standard normal curve is graphed below. shade the region under the standard normal curve to the left of ( z = 0.00 ).
(b) use this table or the aleks calculator to find the area under the standard normal curve to the left of ( z = 0.00 ).
give your answer to four decimal places (for example, 0.1234).

Explanation:

Step1: Recall the property of the standard normal distribution

The standard normal distribution \(Z\sim N(0,1)\) is symmetric about \(z = 0\). The total area under the standard normal curve is \(1\).

Step2: Calculate the area to the left of \(z = 0.00\)

By the symmetry property of the standard normal distribution, the area to the left of \(z=0\) is \(\frac{1}{2}\).

Answer:

\(0.5000\)