Answer:
Standard Deviation = 9.1
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Step-by-step explanation:
Standard deviation = square root of variance
= = 9.1
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Answer:
63% of the values lies between 70 and 85.
Step-by-step explanation:
We are given that a normally distributed set of numbers has a mean of 75 and a standard deviation of 7.97.
<em>Let X = Set of numbers</em>
The z-score probability distribution for is given by;
Z = ~ N(0,1)
where, = mean value = 75
= standard deviation = 7.97
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
So, percentage of values that lies between 70 and 85 is given by = P(70 < X < 85) = P(X < 85) - P(X 70)
P(X < 85) = P( <
) = P(Z < 1.25) = 0.89435 {using z table}
P(X 70) = P(
) = P(Z
-0.63) = 1 - P(Z < 0.63)
= 1 - 0.73565 = 0.26435
<em>Now, in the z table the P(Z </em><em> x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.25 and x = 0.63 in the z table which has an area of 0.89435 and 0.73565 respectively.</em>
Therefore, P(70 < X < 85) = 0.89435 - 0.26435 = 0.63 or 63%
<em>Hence, 63% of the values lies between 70 and 85.</em>
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Let's solve this inequality.
First of all, let's move all the numbers to the right, using the :
Now, let's move the variables to the left:
Now, as you can see, we ended up with a false statement. 0 is NOT greater than 5.
Thus, there are no values of x that make the inequality true, and the inequality has
Hope you find it helpful.
Feel free to ask if you have any doubts.