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.

Question

Mathematics

Hana Clayton

15 February, 10:24

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.

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Answers (1)

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Hanson · Answer 1

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