A normally distributed random variable X is converted to Z. Find P(−2 < Z < 3). Note: Report the answer as a number rounded off to two digits after the decimal point.

To find the probability that Z is between -2 and 3, we need to use the standard normal distribution table or Z-table.

The Z-table gives us the probability that a standard normal random variable Z is less than a given value.

1. First, we find the probability that Z is less than 3, which is P(Z < 3). Looking up 3.00 in the Z-table, we find that this probability is 0.9987.

2. Next, we find the probability that Z is less than -2, which is P(Z < -2). Looking up -2.00 in the Z-table, we find that this probability is 0.0228.

3. To find the probability that Z is between -2 and 3, we subtract the probability that Z is less than -2 from the probability that Z is less than 3: P(-2 < Z < 3) = P(Z < 3) - P(Z < -2) = 0.9987 - 0.0228 = 0.9759.

So, the probability that Z is between -2 and 3 is approximately 0.98 when rounded off to two digits after the decimal point.