Question

Standard Normal Distribution Variable z follows the standard normal distribution. For each of the following parts, make a pencil sketch of the distribution \& your finding. Using 4 decimal places, find:

P(z≤−2.5); [use NORM.S.DIST (∙,1)]

Answer 1

The standard normal distribution has a mean of 0 and a standard deviation of 1. To find P(z ≤ -2.5) in a standard normal distribution, you can use the NORM.S.DIST function with a z-score of -2.5. The resulting probability is approximately 0.0062.

Step-by-step explanation:

The standard normal distribution is a type of normal distribution with a mean of 0 and a standard deviation of 1. It is represented as Z ~ N(0, 1). The z-score of a value x from a normal distribution N(µ, σ) tells us how many standard deviations x is above or below the mean.

To find P(z ≤ -2.5) using the NORM.S.DIST function in Excel with a standard normal distribution, you would use the formula: NORM.S.DIST(-2.5, 1). Calculating this gives a result of approximately 0.0062.

Therefore, the probability that a value from the standard normal distribution is less than or equal to -2.5 is approximately 0.0062.