Questions: The area of the shaded region is .1685.

The area of the shaded region is .1685.
Transcript text: The area of the shaded region is .1685 $\square$ .
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Solution

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Solution Steps

Step 1: Finding the area for part (b)

The shaded area represents the probability $P(Z < -0.96)$. To find this probability using a TI-84 Plus calculator, we can use the normalcdf function. The syntax for this function is normalcdf(lower bound, upper bound, mean, standard deviation). Since the standard normal distribution has a mean of 0 and a standard deviation of 1, and the lower bound is negative infinity, we can use a large negative number like -1E99 (which represents $-1 \times 10^{99}$) as the lower bound. The upper bound is -0.96. normalcdf(-1E99, -0.96, 0, 1) returns approximately 0.1685.

Step 2: Finding the area for part (c)

The shaded area represents the probability $P(-0.35 < Z < 1.89)$. To find this probability using a TI-84 Plus calculator, we can use the normalcdf function with a lower bound of -0.35 and an upper bound of 1.89, mean 0 and standard deviation 1. normalcdf(-0.35, 1.89, 0, 1) which returns approximately 0.6023.

Final Answer:

The area of the shaded region in (b) is 0.1685. The area of the shaded region in (c) is 0.6023.

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