A normal distribution has a mean of 103 and a standard deviation of 12. Find the probability that a value selected at random is in the following interval.
at least 79
The probability that a value selected at random is in the given interval is
enter your response here%.
(Type an integer or a decimal.)
To find the probability that a value selected at random is at least 79, we need to calculate the z-score for 79 using the formula:
z = (X - μ) / σ
where:
X = 79 (value)
μ = 103 (mean)
σ = 12 (standard deviation)
z = (79 - 103) / 12
z = -2
Next, we find the probability using a standard normal distribution table or calculator. The probability of a z-score less than -2 is approximately 0.0228.
However, we are interested in the probability of a value being at least 79, which corresponds to the area to the right of z = -2. Therefore, the probability is 1 - 0.0228 = 0.9772 or 97.72%.
Therefore, the probability that a value selected at random is at least 79 is 97.72%.