Question

Estimate your average commute time from your residence to school in minutes. Let this estimated commute time in minutes (30) represent the population mean (μ), and assume a standard deviation (σ) of 7.51 minutes. Then, find the probability for the following scenarios.

What is the probability that your commute time is less than 15 minutes?

What is the probability that your commute time is greater than 35 minutes?

What is the probability that your commute time is between 15 minutes and 35 minutes?

Answer 1

Z score normal distribution Formula:

z = (x - μ) / σ

What is the probability that your commute time is less than 15 minutes?

z = (15-30)/7.51 = -2

P(Z < -2) = 0.0228

Us FC Area from a value (Use to compute p from Z) Value from an area (Use to compute Z for confidence intervals) Specify Parameters: Mean 0 SD 1 Above 1.96 Below -2 Between -1.96 O Outside -1.96 and 1.96 and 1.96 Results: Area (probability) 0.0228000001

What is the probability that your commute time is greater than 35 minutes?

z = (35-30)/7.51 = 0.67

P(Z > 0.67) = 0.2514

3 Area from a value (Use to compute p from Z) Value from an area (Use to compute Z for confidence intervals) Specify Parameters: Mean 0 SD 1 Above 0.67 Below -2 Between -1.96 Outside - 1.96 and 1.96 and 1.96 Results: Area (probability) 0.2514

What is the probability that your commute time is between 15 minutes and 35 minutes?

P(-2 < z < 0.67) = 0.7258

Area from a value (Use to compute p from Z) Value from an area (Use to compute Z for confidence intervals) Specify Parameters: Mean O SD 1 Above 0.67 Below -2 Between -2 Outside -1.96 and 0.67 and 1.96 Results: Area (probability) 0.7258