Suppose you draw a value each day at random from a normal distribution with a mean of 0 and a standard deviation of How many days should it take on average for you to draw a value that's greater than 2?
Question Analysis
This question is about understanding a normal distribution and calculating the probability of a random event. Here, you are drawing a value each day from a normal distribution with a mean of 0. However, the standard deviation is not specified, which could be a typographical error. Typically, the standard deviation is crucial for calculations involving normal distributions. For the sake of this problem, let's assume the standard deviation is 1, as is often the case in standard normal distributions. The question asks for the average number of days it would take to draw a value greater than 2.
To solve this, you need to:
- Understand that the problem is asking for the expected number of trials to get a success (drawing a value greater than 2).
- Use the properties of the normal distribution and the concept of probability.
Answer
To find the expected number of days to draw a value greater than 2, consider the following steps:
-
Calculate the Probability:
- We need the probability of drawing a value greater than 2 from a standard normal distribution (mean = 0, standard deviation = 1).
- Use the Z-table (standard normal distribution table) or a calculator to find this probability.
- The Z-score for a value of 2 is 2 (since Z = (X - mean) / standard deviation = (2 - 0) / 1 = 2).
- From the Z-table, the probability (P(Z > 2)) is approximately 0.0228.
-
Calculate the Expected Number of Days:
- The expected number of days to get a value greater than 2 is the inverse of the probability of drawing such a value.
- This is calculated by taking the reciprocal of the probability: ( \frac{1}{0.0228} \approx 43.86 ).
Therefore, on average, it should take approximately 44 days to draw a value greater than 2 from this normal distribution.