MULTIPLE CHOICE A triangle has an angle that measures 41° and an angle
2 answers:
You might be interested in
Answer:
a) The expected value of the sample mean weight is 20.4 pounds.
b)The standard deviation of the sample mean weight is 0.123.
c) There is a 14.46% probability the sample mean weight will be less than 20.27.
d) This value is .
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation
.
Problems of normally distributed samples can be 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:
A particular variety of watermelon weighs on average 20.4 pounds with a standard deviation of 1.23 pounds. This means that
Consider the sample mean weight of 100 watermelons of this variety. This means that .
a. What is the expected value of the sample mean weight? Give an exact answer.
By the Central Limit Theorem, it is the same as the mean of the population. So the expected value of the sample mean weight is 20.4 pounds.
b. What is the standard deviation of the sample mean weight? Give your answer to four decimal places.
By the Central Limit Theorem, that is:
The standard deviation of the sample mean weight is 0.123.
c. What is the approximate probability the sample mean weight will be less than 20.27?
This is the pvalue of Z when .
Since we are working with the sample mean, we use instead of
in the Z score formula
has a pvalue of 0.1446.
This means that there is a 14.46% probability the sample mean weight will be less than 20.27.
d. What is the value c such that the approximate probability the sample mean will be less than c is 0.96?
This is the value of that is in the 96th percentile, that is, it's Z score has a pvalue 0.96.
So we use
This value is .
Answer:
Step-by-step explanation:
Flipping a coin and rolling a number cube are both independent events. Independent events do not rely on the outcome of any previous events. This means that whatever you flip on the coin will have no effect on whatever you roll on the number cube and each flip of the coin or roll of the cube has the same probability as the flip or roll before.
The probability of getting tails on a coin toss is:
The probability of getting a number less than 3 (so 1 or 2) on a number cube is:
Since we are combining these events, we need to multiply the fractions together to get our overall probability:
*
=