Complete Question
The complete question is shown on the first uploaded image
Answer:
The sales level that is the cut-off between quarters that are considers as "failure" and those that are not is evaluated as
Step-by-step explanation:
From the question we are told that the
Mean is
Standard deviation is
Let Y be the random variable that denotes the sales made quarterly among health care information system
The normal distribution for this data is mathematically represented as
~ N
From the question we are told that a quarter is consider a failure by the company if the sales level that quarter in the bottom 10% of the of all quarterly sales
So
The the Probability of obtaining quarterly sales level that is equal to 10% of all quarterly sale (It is not below 10%) is mathematically represented as
This can be represented as a normal distribution in this manner
Where ~
{This mean that this equal to the normal distribution between 0, 1 which is the generally range of every probability }
Therefor we have
The cumulative distribution function for a normal distribution of y is mathematically represented as
This is because a cumulative distribution function of a random value Y or a distribution of Y evaluated at y is the probability that Y will take will take a value that is less or equal to y
Calculating the inverse of the cumulative distribution function value of 0.10 which is negative the the critical value(Critical values determine what probability a particular variable will have when a sampling distribution is normal or close to normal.) of 0.01