Suppose that a random variable has a standard normal distribution. use a standard normal table such as this one to determine the probability that is between −1 and 0.67. give your answer in decimal form, precise to at least three decimal places.

The probability That is between -1 and 0.67 is 0.58991

Step-by-step explanation:

* Lets explain how to solve it

- A random variable has a standard normal distribution

- Z-scores are -1 and 0.67

- We need to find the probability that is between them by using the

  standard normal table

- Search in the table of the standard normal distribution for the

 corresponding area of -1 and corresponding area of 0.67

- From the standard normal distribution table we find that

∵ The corresponding area which represents z = -1 is 0.15866

∵ The corresponding area which represents z = 0.67 is 0.74857

- To find the probability between -1 and 0.67 find the difference

  between the corresponding areas of -1 and 0.67

∵ z = -1 represented by 0.15866

∵ z = 0.67 represented by 0.74857

∴ The difference of the corresponding areas is:

   0.74857 - 0.15866 = 0.58991

∴ The probability that is between -1 and 0.67 is 0.58991

the image is given below

since the options are not given so we draw it from the equation

the given equation is

y = (x-1) (x+4)

y = y² + 3x - 4

the above equation is a quadratic equation which will have two roots. if we draw the graph for it, it will look like this