The formula means that first, we sum the square of each value times its probability then subtract the square of the mean. Let us check the below points, which help us summarize the key learnings for this topic of probability. The probability that X is equal to any single value is 0 for any continuous random variable (like the normal). What makes you think that this is not the right answer? The theoretical probability calculates the probability based on formulas and input values. The probability of a random variable being less than or equal to a given value is calculated using another probability function called the cumulative distribution function. If you scored a 60%: \(Z = \dfrac{(60 - 68.55)}{15.45} = -0.55\), which means your score of 60 was 0.55 SD below the mean. Imagine taking a sample of size 50, calculate the sample mean, call it xbar1. Entering 0.5 or 1/2 in the calculator and 100 for the number of trials and 50 for "Number of events" we get that the chance of seeing exactly 50 heads is just under 8% while the probability of observing more than 50 is a whopping 46%. this. The rule is a statement about normal or bell-shaped distributions. The z-score is a measure of how many standard deviations an x value is from the mean. When we write this out it follows: \(=(0.16)(0)+(0.53)(1)+(0.2)(2)+(0.08)(3)+(0.03)(4)=1.29\). In terms of your method, you are actually very close. Find the area under the standard normal curve to the left of 0.87. The formula means that we take each value of x, subtract the expected value, square that value and multiply that value by its probability. Therefore, the CDF, \(F(x)=P(X\le x)=P(X