Find the value of a if: P(Z < a) = 0.0359
In order to find the value of "a", we need to use a standard normal distribution table or a calculator that provides values for the cumulative distribution function (CDF) of the standard normal distribution.
The given probability, P(Z < a) = 0.0359, indicates that we want to find the value of "a" such that the area to the left of "a" under the standard normal curve is 0.0359.
Looking up this value in a standard normal distribution table, we find that the corresponding z-score is approximately -1.81.
Therefore, a = -1.81.
To find the value of "a" such that P(Z < a) = 0.0359, we need to use the standard normal distribution table or a calculator.
The standard normal distribution table gives us the probability of the standard normal random variable Z being less than a given value. Since the standard normal distribution is symmetric around the mean of 0, we can use the table to find the value corresponding to the desired probability of 0.0359.
Looking up the value 0.0359 in the standard normal distribution table, we find that it corresponds to approximately -1.812.
Therefore, the value of "a" that satisfies P(Z < a) = 0.0359 is a ≈ -1.812.
To find the value of "a," we need to look up the corresponding z-score for the given probability.
The z-score represents the number of standard deviations a data point is from the mean in a standard normal distribution (Z-distribution). In this case, we are looking for "a" such that P(Z < a) is equal to 0.0359.
Step 1: Determine the critical value or z-score using a standard normal distribution table or a statistical calculator.
The value 0.0359 represents the area under the standard normal curve to the left of "a." We refer to this as the cumulative probability.
By looking up the z-score in a standard normal distribution table or using a statistical calculator, we can find the critical value associated with this probability.
Let's assume that the standard normal distribution table gives a critical value of -1.81 for a cumulative probability of 0.0359.
Step 2: Determine the value of "a" using the critical value or z-score.
The z-score represents the number of standard deviations from the mean. Therefore, by substituting the critical value back into the equation, we can solve for "a."
a = z * standard deviation + mean
In a standard normal distribution, the mean (μ) is always 0, and the standard deviation (σ) is always 1.
So, in this case, a = -1.81 * 1 + 0 = -1.81.
Thus, the value of "a" for P(Z < a) = 0.0359 is approximately -1.81.