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The probability that a randomly selected programmer major received a salary less than 38000 is 0,3085
Step-by-step explanation:
We will assume that the salaries are Normally distributed. Lets call X the salary of a random major programmer in dollars. We want the pprobability of X being less than 38000. For it, we will standarize X. Lets call W the standarization, given by the formula
Lets denote the cumulative distribution function of the standard normal variable W. The values of
are well known and they can be found in the attached file. Now, lets calcualte the probability of X being less than 38000 using
Since the density function of a standard normal random variable is symmetric, then
The probability that a randomly selected programmer major received a salary less than 38000 is 0,3085.