Please, answer with the full solution! Thanks for the help!

Readings on a thermometer are normally distributed with a mean of 0C and a standard deviation of 1.00.

What is the probability that a randomly selected
thermometer reads:
• Less than 0.53.
• Greater than -0.11
• Greater than -1.11
• Between 1.00 and 2.25
• Between -2.28 and -1.76
• Between -1.33 and 1.86
• Greater than 1.71

Question

Please, answer with the full solution! Thanks for the help!

Readings on a thermometer are normally distributed with a mean of 0C and a standard deviation of 1.00.

What is the probability that a randomly selected
thermometer reads:
• Less than 0.53.
• Greater than -0.11
• Greater than -1.11
• Between 1.00 and 2.25
• Between -2.28 and -1.76
• Between -1.33 and 1.86
• Greater than 1.71

mhchen · Answer

Do you know how to find the percentage of the distribution using z-scores?

Once you have the percentages, those are your probability.

giovxnnx · Answer

I am asking for someone to kindly solve them for me, it is really important and I have a real reason to not being able to solve them by myself. I am sorry. Please, help Mhchen.

owen3 · Answer

You can use a normal distribution calculator, which are on the web.

owen3 · Answer

http://www.wolframalpha.com/widgets/view.jsp?id=98b17f068d5d9b7668e19fb8ae470841

owen3 · Answer

I can walk you through using the calculator.

giovxnnx · Answer

@owen3 I really did not understand a thing on how this calculator function and where I should put each number! Plus, I need to write down on paper the whole solution for each. Thanks anyway!

owen3 · Answer

You can't really do it by hand, it involves an integral. You need a table or a calculator.

directrix · Answer

I found the z-score that corresponds with the .53 reading.

z = (x - mean) / standard deviation

z = (.53 - 0) / 1

z = .53

Go to Normal Distribution Area Under the Curve Table.

Find .53.

Read out the area under the curve to the left of z = .53.

That is the probability.

.7019 = area

Roughtly, 70% of the time the thermometer will read less than .53.

directrix · Answer

To get the areas under the curve, I use the chart rather than the calculator.

directrix · Answer

Here is a place to read about the procedure. http://accounts.smccd.edu/moss/Personal/math_200/Lecture%20Notes/Chapter%206_2.pdf @giovxnnx

mathmale · Answer

"Please, answer with the full solution!" is totally inappropriate here.  You can ask for guidance that will help you solve the problem yourself, but asking for a direct answer with no involvement of yourself is strictly a NO-NO.