# Find the probability that a randomly selected thermometer reads less than 0.53 and draw a sketch of the regionsAssume the readings in thermometers are normally distributed with a mean of `0^@` C...

Find the probability that a randomly selected thermometer reads less than 0.53 and draw a sketch of the regions

Assume the readings in thermometers are normally distributed with a mean of `0^@` C and standard deviation of `1^@` C

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### 1 Answer

Given `mu=0,sigma=1` :

(1) Find the probability that a randomly selected thermometer reads less than 0.53. (`P(x<0.53)` )

First we convert the reading to a standard normal score using `z=(x-mu)/sigma` . We get `z=(0.53-0)/1=.53`

Using the standard normal table we find the area to the left of z=.53 to be .7019 (A calculator gives .7019440569) ** Some standard normal tables do not give the area to the left of a z value; some give are to 0, etc... Know which type of table you have**

The area to the left of a z score is also the probability that a randomly selected score will be to the left of the given score.

So `P(x<0.53)=P(z<0.53)~~.7019`

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**The probability that a random thermometer has a reading less than 0.53 is approxiamtely .7019**

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(2) I cannot draw the picture on this site.

Draw a standard normal curve with mean=0. Draw a vertical segment at x=.53 from the x-axis to the curve, then shade the area under the curve to the left of the segment.

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