Question

Hi, im stuck on this standard normal distribution.

I must use excel function and the cells to calculate these problems.

7.)What is the probability Z is less than -1.96 (i.e. P(X < -1.96)

8.)What is the probability X is greater than 1.96 (i.e. P(X > 1.96)

9.)What is the probability X is between -1.645 and 1.645 (i.e. P(-1.645 < X < 1.645) Assume Z is a standard normally distributed random variable. 3 Z-N(0, 1) Mean Std Dev 4 0 1 5 # 6 P(Z<#) 7 P(Z>#) Probability -1.96 7) What is the probablity Z is less than -1.96 (i.e. P(X<-1.96)? 1.96 8) What is the probablity X is greater than 1.96 (i.e. P(X>1.96)? -1.645 1.645 9) What is the probablity X is between-1.645 and 1.645 (i.e. P(-1.645

Answer 1

To calculate the probabilities using Excel:)

1. To find the probability that Z is less than -1.96 (P(X < -1.96)), you can use the formula =NORM.DIST(-1.96,0,1,TRUE). This formula will give you the cumulative probability up to -1.96.

2. To find the probability that X is greater than 1.96 (P(X > 1.96)), you can subtract the probability of X being less than or equal to 1.96 from 1. To do this, you can use the formula =1-NORM.DIST(1.96,0,1,TRUE). This formula will give you the complement of the cumulative probability up to 1.96.

3. To find the probability that X is between -1.645 and 1.645 (P(-1.645 < X < 1.645)), you can subtract the probability of X being less than or equal to -1.645 from the probability of X being less than or equal to 1.645. You can use the formula =NORM.DIST(1.645,0,1,TRUE)-NORM.DIST(-1.645,0,1,TRUE). This formula will give you the difference between the cumulative probabilities up to 1.645 and -1.645.

Remember to replace the mean and standard deviation values in the NORM.DIST function with the appropriate values for your problem. In this case, since Z is a standard normally distributed random variable, the mean is 0 and the standard deviation is 1.

I hope this helps! Let me know if you have any further questions.