Question
College president receives a housing provision that averages 26234 annually. Assume that a normal distribution applies and that the standard deviation is 5000. What is the probability that a College president will receive an annual housing provision exceeding 35000 per year?
Answers
GPT 3.5
To find the probability that a college president will receive an annual housing provision exceeding $35,000 per year, we need to calculate the z-score and then find the corresponding probability using a standard normal distribution table.
First, we calculate the z-score using the formula:
z = (X - μ) / σ
where:
X = $35,000
μ = $26,234
σ = $5,000
z = (35000 - 26234) / 5000
z = 0.17532
Next, we find the probability of z being greater than 0.17532 using a standard normal distribution table. From the table, we find that the probability corresponding to a z-score of 0.1753 is approximately 0.4306.
Therefore, the probability that a college president will receive an annual housing provision exceeding $35,000 per year is approximately 0.4306, or 43.06%.
First, we calculate the z-score using the formula:
z = (X - μ) / σ
where:
X = $35,000
μ = $26,234
σ = $5,000
z = (35000 - 26234) / 5000
z = 0.17532
Next, we find the probability of z being greater than 0.17532 using a standard normal distribution table. From the table, we find that the probability corresponding to a z-score of 0.1753 is approximately 0.4306.
Therefore, the probability that a college president will receive an annual housing provision exceeding $35,000 per year is approximately 0.4306, or 43.06%.