Final answer:
To calculate the probability of profit greater than zero for normally distributed stock profits, find the z-score for profit at zero and use standard normal distribution tables or a calculator to find the corresponding probability.
Step-by-step explanation:
To determine the probability that the profit from a single randomly selected stock is greater than zero, when the profits are normally distributed with a mean of 1 and a standard deviation of 5, we can use the concept of a z-score. The z-score is a measure of how many standard deviations an element is from the mean. In this case, we want to calculate the probability that the profit is greater than zero, we start by finding the z-score for a profit of zero using the formula:
Z = (X - μ) / σ
where X is the value of the profit (in this case, 0), μ (mu) is the mean, and σ (sigma) is the standard deviation. Substituting the values in:
Z = (0 - 1) / 5 = -0.2
Using standard normal distribution tables or a calculator, we can find the probability that z is greater than -0.2. This is equivalent to 1 minus the probability of z being less than -0.2. The value from the tables or calculator gives us the area to the left of z=-0.2. To find the area to the right (the probability of profit greater than zero), we subtract this value from 1.
The result gives us the probability that the profit is greater than zero. This process uses the properties of the standard normal distribution, which assumes that the median and the mean are the same, therefore, the normal distribution is symmetric around the mean.