Discrete Variable/Normal Distribution Challenge Worksheet
1. A discrete random variable X has the probability distribution shown below, with one value missing. The standard deviation of the variable is σ = 3.816. Find the missing value of X, rounded to the nearest integer. Hint: You will need the quadratic formula!
X P(X)
0 0.5
4 0.3
??? 0.2
2. The NYPD reports that the average time it takes to respond to an emergency call in New York City is 25 minutes. Assume response time is normally distributed. Response time is considered ”too slow” if the time exceeds 30 minutes, and about 11% of all repsonse times are categorized as ”too slow”. What is the standard deviation of response time?
