To find: the indicated probability for a randomly selected x-value from the distribution using the standard normal table.
Given information:
The probability to be found is:
It is given that the distribution is normal and has mean
Concept Used:
Standard
The standard normal distribution is the normal distribution with mean 0 and standard deviation1. The formula below can be used to transform x-values from a normal distribution with mean
The z-value for a particular x-value is called the z-score for the x-value and is the number of standard deviations the x-value lies above or below the mean
Standard Normal Table
If z is a randomly selected value from a standard normal distribution, the table below can be used to find the probability that z is less than or equal to some given value.
Standard Normal Table | ||||||||||
z | .0 | .1 | .2 | .3 | .4 | .5 | .6 | .7 | .8 | .9 |
-3 | .0013 | .0010 | .0007 | .0005 | .0003 | .0002 | .0002 | .0001 | .0001 | .0000+ |
-2 | .0228 | .0179 | .0139 | .0107 | .0082 | .0062 | .0047 | .0035 | .0026 | .0019 |
-1 | .1587 | .1357 | .1151 | .0968 | .0808 | .0668 | .0548 | .0446 | .0359 | .0287 |
-0 | .5000 | .4602 | .4207 | .3821 | .3446 | .3085 | .2743 | .2420 | .2119 | .1841 |
0 | .5000 | .5398 | .5793 | .6179 | .6554 | .6915 | .7257 | .7580 | .7881 | .8159 |
1 | .8413 | .8643 | .8849 | .9032 | .9192 | .9332 | .9452 | .9554 | .9641 | .9713 |
2 | .9772 | .9821 | .9861 | .9893 | .9918 | .9938 | .9953 | .9965 | .9974 | .9981 |
3 | .9987 | .9990 | .9993 | .9995 | .9997 | .9998 | .9998 | .9999 | .9999 | 1.0000- |
Explanation:
Now, to find
So, first step is to find
For that, first find the z-score corresponding to the x-value of 80.
Now, to find this value, find the intersection point where row -2 and column .1 intersects.
The table shows that:
Next step is to find
First step is to find the z-score corresponding to the x-value of 50.
Now, it is known that the z-value for a particular x-value is called the z-score for the x-value and is the number of standard deviations the x-value lies above or below the mean
Here
So,
It can be observed by looking at the standard normal table that for
That is, the probability
So, the required probability is:
Chapter 6 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
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