The average number of spectators at a football competition for the first five days was 3,144.The attendance on the sixth day was
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Answer:
73.30% probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce
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 sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
What is the probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce?
This is the pvalue of Z when X = 8.2 + 0.02 = 8.22 subtracted by the pvalue of Z when X = 8.2 - 0.02 = 8.18. So
X = 8.22
By the Central Limit Theorem
has a pvalue of 0.8665
X = 8.18
has a pvalue of 0.1335
0.8665 - 0.1335 = 0.7330
73.30% probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce
In the congruent triangles both triangle are same . In this triangle 2.3.3 congruent triangle image given below to understand better.
According to the question, given that
2.3.3 congruent triangle under congruence triangle are explain:
Both triangles are said to be congruent if the three angles and three sides of one triangle match the corresponding angles and sides of the other triangle. We can see from the examples PQR and XYZ that PQ = XY, PR = XZ, and QR = YZ, and thus P = X, Q = Y, and R = Z. Then, we can state that XYZ and PQR.
To be congruent, the two triangles must be the same size and shape. It is necessary for both triangles to be superimposed on one another. A triangle appears to be in a different place or have a different look as we rotate, reflect, and/or translate it.
Two triangles must meet five requirements in order to be congruent. The congruence properties are SSS, SAS, ASA, AAS, and RHS.
SSS Congruence Criteria
Side-Side-Side criterion is referred to as the SSS criterion. According to this standard, two triangles are congruent if their respective triangles' three sides are equal to one another.
The three angles of BAC must be identical to the corresponding angles of XYZ if, according to the SSS condition, BAC XYZ.
SAS Congruence Criteria
Side-Angle-Side criterion is referred to as the SAS criterion. According to this standard, two triangles are said to be congruent if their matching sides and included angles are the same on each side of each other.
The third side (AB) and the other two angles of ABC must be identical to the equivalent side (XY) and the angles of XYZ if ABC XYZ under the SAS condition.
ASA Congruence Criteria
Angle-Side-Angle criterion is also known as ASA criterion. According to the ASA criterion, two triangles are congruent if any two of their included sides and related angles are equivalent in size to those of the other triangle.
AAS Congruence Criteria
Angle-Angle-Side criterion is also known as the AAS criterion. Two triangles are said to be congruent according to the AAS criterion if any two angles and the non-included side of one triangle match the corresponding angles and side of the second triangle.
RHS Congruence Criteria
Right angle-hypotenuse-side congruence is referred to as the RHS criterion. If the hypotenuse and side of one right-angled triangle are equal to the hypotenuse and the corresponding side of another right-angled triangle, then two triangles are said to be congruent according to this criterion.
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