# I Probability - z value

#### rexxii

Summary
Probability - z value - stats issue
Hi,

I'm working on a question now where I need to calculate the z value. which I have been able to but I'm calculating a value off the normal distribution that is on the left-hand side of the normal distribution curve and it needs to on the right side. As the value i'm looking into is higher than the mean!

I cannot figure out how I would turn this around. its only one independent event theres no replacement or other variables.

the question is:

A cable manufacturer tests the cables it produces to find the breaking load. Over many years this has been assumed to be normally distributed with a mean of 6000 newtons and standard deviation of 155 newtons. Calculate the probability that a single cable chosen at random, will have a breaking load greater than 6200 N.

Z = 6200 -6000 /155 = 1.29

Then ive written a probability statement (P z>1.290) = P z>1.290)

read from the stats tables that it could be 0.9015.

Said the breaking load is 90.15%

The probability that a randomly selected cable will have a breaking load greater breaking load than 6200 Newtons is 90%.

Last edited by a moderator:

#### Mark44

Mentor
Summary: Probability - z value - stats issue

Hi,

I'm working on a question now where I need to calculate the z value. which I have been able to but I'm calculating a value off the normal distribution that is on the left-hand side of the normal distribution curve and it needs to on the right side. As the value i'm looking into is higher than the mean!

I cannot figure out how I would turn this around. its only one independent event theres no replacement or other variables.

the question is:

A cable manufacturer tests the cables it produces to find the breaking load. Over many years this has been assumed to be normally distributed with a mean of 6000 newtons and standard deviation of 155 newtons. Calculate the probability that a single cable chosen at random, will have a breaking load greater than 6200 N.

Z = 6200 -6000 /155 = 1.29

Then ive written a probability statement (P z>1.290) = P z>1.290)

read from the stats tables that it could be 0.9015.
You're reading the table wrong. The table is giving you P(z < 1.290) = 0.9015. So what would be the probability you want, P(z > 1.290)?
rexxii said:
Said the breaking load is 90.15%

The probability that a randomly selected cable will have a breaking load greater breaking load than 6200 Newtons is 90%.

#### rexxii

So i need to read from the RHS side? as it is above the mean? Would i still select that number or a different one of the table?

#### Mark44

Mentor
P(z < 1.290) = .9015, from the table. The number .9015 represents the area under the standard normal curve between $z = -\infty$ and z = 1.290. What is the total area under the curve? What's the area under the curve between z = 1.290 and $z = +\infty$?

#### rexxii

1.29 - 1 = 0.29 above the mean?

#### Mark44

Mentor
1.29 - 1 = 0.29 above the mean?
No, and this doesn't make any sense -- you're mixing two unrelated things there: the z-value and the probability associated with a certain z-value.

Have you seen a graph of the standard normal curve? In the standard normal distribution, half of the area under the curve is to the left of the mean at z = 0, and the other half is to the right. What's the total area under the curve? How much of the area under the curve lies to the left of z = 1.29? How much of the area lies to the right of z = 1.29?

It would be a good idea to read the section in your textbook that has this problem. There's quite a bit you don't understand.

"Probability - z value"

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