The function R(x) + S(x) exists given by .
An expression, rule, or law that describes a relationship between one variable (independent variable) and another variable (dependent variable) exists named a function.
Let the functions be and
Adding both of the equations, we get
simplifying both of the equations we get
Therefore, the function R(x) + S(x) exists given by .
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Answer:
47.06% of the population has an IQ between 85 and 105.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
What percent of the population has an IQ between 85 and 105?
This is the pvalue of Z when X = 105 subtracted by the pvalue of Z when X = 85. So
X = 105
has a pvalue of 0.6293.
X = 85
has a pvalue of 0.1587
So 0.6293 - 0.1587 = 0.4706 = 47.06% of the population has an IQ between 85 and 105.
Answer: 0.81859
Step-by-step explanation:
Using the formula ;
Z =
where u = mean
Therefore the probability that a student will finish the test between 40 and 70 will be :
P ( 40≤X≤70 ) = P(X≤70) - P(X≤40)
P ( 60-40/10) , P( 60 - 70 / 10)
= 2 , -1
= P (Z ≤ 2) - P( Z ≤ -1 )
From normal table , we have
0.97725 - 0.15866
Therefore the probability that a student will finish the test between 40 and 70 minutes = 0.81859