Questions: Find the indicated probability using the standard normal distribution. P(0<z<0.665) Click here to view page 1 of the standard normal table. Click here to view page 2 of the standard normal table. P(0<z<0.665)= (Round to four decimal places as needed.)

Solution Steps

To find the probability \( P(0 < z < 0.665) \) using the standard normal distribution, we need to calculate the cumulative distribution function (CDF) for \( z = 0.665 \) and subtract the CDF for \( z = 0 \). The CDF gives the probability that a standard normal random variable is less than or equal to a given value. Since the CDF for \( z = 0 \) is 0.5, we can use this to find the desired probability.

To find the probability \( P(0 < z < 0.665) \), we first calculate the cumulative distribution function (CDF) for \( z = 0.665 \). The CDF value is approximately \( 0.7470 \).

The CDF for \( z = 0 \) in a standard normal distribution is \( 0.5 \).

The probability \( P(0 < z < 0.665) \) is given by the difference between the CDF values calculated in the previous steps: \[ P(0 < z < 0.665) = \text{CDF}(0.665) - \text{CDF}(0) = 0.7470 - 0.5 = 0.2470 \]

Final Answer