If a sample of size 30 is selected, the value of A for the probability p(>- A) = 0.01 is?
To find the value of A for the probability p(>-A) = 0.01, we can use the Z-score table.
Step 1: Identify the confidence level (1 - probability) that corresponds to the p-value given. In this case, p(>-A) has a probability of 0.01, so the confidence level is 1 - 0.01 = 0.99.
Step 2: Look up the Z-score corresponding to the desired confidence level in the Z-score table. The Z-score represents the number of standard deviations away from the mean.
For a 0.99 confidence level, the Z-score is approximately 2.33.
Step 3: Use the formula A = Z * (σ / √n) to find the value of A, where Z is the Z-score, σ is the standard deviation, and n is the sample size.
However, since the standard deviation (σ) is not provided, we cannot calculate the exact value of A without additional information.
To find the value of A for the given probability, we need to refer to the standard normal distribution table or use a statistical calculator.
Step 1: Convert the given probability to a z-score. The z-score represents the number of standard deviations a value is from the mean in a standard normal distribution.
For p(>-A) = 0.01, we want to find the z-score corresponding to a cumulative probability of 1 - 0.01 = 0.99. This is because the table typically shows cumulative probabilities up to the left tail, and we want to find the value for the right tail.
Step 2: Look up the z-score in the standard normal distribution table or use a statistical calculator.
For a cumulative probability of 0.99, the corresponding z-score is approximately 2.33 (rounding to two decimal places).
Step 3: Convert the z-score back to the value of A using the formula:
A = z * (standard deviation / square root of sample size)
Since we don't know the standard deviation of the population, we use an estimate, called the standard error (SE), which is the standard deviation of the sample divided by the square root of the sample size.
Assuming you have the standard deviation of the population or the standard error, you can plug in the values in the formula to find the value of A. However, in this case, since we don't have the standard deviation or the standard error, we cannot determine the exact value of A.
To summarize: Without the standard deviation or the standard error, it is not possible to calculate the exact value of A for the probability p(>-A) = 0.01.