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

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
![P[Y < y ] = 0.10](https://img.qammunity.org/2021/formulas/mathematics/college/u24hqnp4vn3e8ifmfznjic63jtpza4vrdb.png)
This can be represented as a normal distribution in this manner
![P [ (Y- \mu)/(\sigma ) < (y -\mu)/(\sigma) ] = 0.10](https://img.qammunity.org/2021/formulas/mathematics/college/zlsfrhbcguz37xlh7g61ogestw6hwepkxu.png)
Where
~
{This mean that this equal to the normal distribution between 0, 1 which is the generally range of every probability }
Therefor we have
![P[Z < (y- 8)/(1.3) ]](https://img.qammunity.org/2021/formulas/mathematics/college/a6cx297ntazin124o6fndpk4hv48cclx7c.png)
The cumulative distribution function for a normal distribution of y is mathematically represented as
![\phi [(y- 8)/(1.3) ] = 0.10](https://img.qammunity.org/2021/formulas/mathematics/college/vx5k9lt7j0bxlqnoomrq1nvf03b5xwwsxx.png)
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
![\phi ^(-1)(0.10) =- [1 - (0.10)/(2)]](https://img.qammunity.org/2021/formulas/mathematics/college/xlymm5o9pokv0nbtq4qbl50e4wx2jvvzsh.png)



