Renee scores an average of 153 points in a game of bowling, and her points in a game of bowling are normally distributed. suppose renee scores 175 points in a game, and this value has a z-score of 2. what is the standard deviation? do not include the units in your answer. for example, if you found that the standard deviation was 15 points, you would enter 15.

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Let X the random variable that represent points in a game of bowling of a population, and for this case we know the distribution for X is given by:

Where and

We know that the value for Renee is X=175 and the z score obteined was Z=2.

Solution to the problem

And the best way to solve this problem is using the normal standard distribution and the z score given by:

We are interested on the value of and we can solv for it:

And replacing the values we have:

step-by-step explanation:

if you want to solve percent error follow these steps.

1. subtract the accepted value from the experimental value.

2. take the absolute value of step 1.

3. divide that answer by the accepted value.

4. multiply that answer by 100 and add the % symbol to express the answer as a percentage.

if you want to solve percent of change just do this.

1. work out the difference (increase) between the two numbers you are comparing.

2. divide the increase by the original number and multiply the answer by 100. if your answer is a negative number then this is a percentage decrease.

hope this : )

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