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We are given that,
and . These are the two probabilities we are going to use in order to find the mean and the standard deviation as follows.
From equation (1),
where is the table value associated with 0.3.
From the standard normal tables, . Therefore,
From equation (2),
We write this equation as,
where, is the table value associated with 0.9. From the standard normal tables, . Therefore,
Equation 3 and 4 are equal so, equating both we have.
We can use either equation (3) or (4) to solve for .Taking equation (3) and substituting for the value of gives,
Therefore, the mean and standard deviation are 50.16 and 19.38 respectively.