The expression for the angle m∠RST from the given bisctor is; 6x - 18
<h3>How to find the expression for a given angle?</h3>From the given image in the attachment we are given that;
SQ bisects ∠TSR
m ∠RSQ = 3x - 9
Now, since SQ is a bisector of ∠TSR, we can say that
m∠RST = 2 * m∠RSQ
Thus angle RST is expressed as;
m∠RST = 2(3x - 9)
m∠RST = 6x - 18
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Answer:
67.30% probability that the mean weight will be between 16.6 and 22.6 lb
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution:
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
Central limit theorem:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
If 4 fish are randomly selected, what is the probability that the mean weight will be between 16.6 and 22.6 lb
This is the pvalue of Z when X = 22.6 subtracted by the pvalue of Z when X = 16.6.
X = 22.6
By the Central Limit Theorem
has a pvalue of 0.8849
X = 16.6
has a pvalue of 0.2119
0.8849 - 0.2119 = 0.6730
67.30% probability that the mean weight will be between 16.6 and 22.6 lb