Questions: Shading a region and Enabling its standard normal probability (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).

Solution Steps

The question asks us to shade the region under the standard normal curve to the left of \(z = 0.00\). Since \(z = 0.00\) represents the mean of the standard normal distribution, shading the area to the left means shading half of the area under the curve.

We are looking for the area under the standard normal curve to the left of \(z = 0.00\). This represents the probability \(P(Z \le 0.00)\), where \(Z\) is a standard normal random variable. Because the standard normal distribution is symmetric around 0, the area to the left of \(z = 0.00\) is 0.5. This can also be confirmed using a standard normal table or calculator.

Final Answer