Answer :
If a random variable "z" follows a standard normal distribution and the probability of "z" being greater than "k" is 0.39, then the value of "k" such that satisfies the equation [p(z > k) = 0.39] will be 0.28
As per the question statement, a random variable "z" follows a standard normal distribution.
We are required to determine the value of "k" such that the equation [p(z > k) = 0.39] is satisfied.
To solve this question, first we will have to calculate the probability of "z" being greater than "k" and then from the Z-table, we will determine the z-score corresponding the above calculated probability value. This z-score will be our desired answer, i.e.,
Given, P(Z > k) = 0.39
Or, P(Z < k) = (1 - 0.39)
Or, P(Z < k) = 0.61
Now, from the Z table, we get the z-score corresponding to probability value of 0.61 is 0.28
Hence, (k = 0.28)
- Normal Distribution: In Statistics and Probability Theory, a normal distribution is the bell-shaped frequency distribution curve of a continuous random variable, based on a set of values of the variable, which lie in a symmetrical fashion majorly situated around their mean and the rest taper off symmetrically toward either extreme.
To learn more about Normal Distributions and Probability, click on the link below.
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