Two number cubes are rolled to determine how a token moves on a game board. The sides of each number cube are numbered 1, 2, 3,
4, 5 and 6.
There are two options describing how the token will be moved.
Option A: If the product is even, move forward 7 spaces. Otherwise, move backward 5.
Option B: If the product is even, move forward 5 spaces. Otherwise, move backward 4.
Use mathematical expectation to determine which option offers the greater likelihood of moving closer to the finish line on the game board.
Which statement best explains the better option?
The mathematical expectation of Option A is 2.75. The mathematical expectation of Option B is 4. Option B offers a greater likelihood of advancing to the finish line.
The mathematical expectation of Option A is 4. The mathematical expectation of Option B is 2.75. Option A offers a greater likelihood of advancing to the finish line.
The mathematical expectation of Option A is 2.75. The mathematical expectation of Option B is 4. Option A offers a greater likelihood of advancing to the finish line.
The mathematical expectation of Option A is 4. The mathematical expectation of Option B is 2.75. Option B offers a greater likelihood of advancing to the finish line.
There are two options describing how the token will be moved.
Option A: If the product is even, move forward 7 spaces. Otherwise, move backward 5.
Option B: If the product is even, move forward 5 spaces. Otherwise, move backward 4.
Use mathematical expectation to determine which option offers the greater likelihood of moving closer to the finish line on the game board.
Which statement best explains the better option?
The mathematical expectation of Option A is 2.75. The mathematical expectation of Option B is 4. Option B offers a greater likelihood of advancing to the finish line.
The mathematical expectation of Option A is 4. The mathematical expectation of Option B is 2.75. Option A offers a greater likelihood of advancing to the finish line.
The mathematical expectation of Option A is 2.75. The mathematical expectation of Option B is 4. Option A offers a greater likelihood of advancing to the finish line.
The mathematical expectation of Option A is 4. The mathematical expectation of Option B is 2.75. Option B offers a greater likelihood of advancing to the finish line.
1 answer:
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Answer:
97.72% probability that their mean body temperature is greater than 98.4degrees° F.
Step-by-step explanation:
To solve this question, we have to understand the normal probability distribution and the central limit theorem.
Normal probability distribution:
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.
Central limit theorem:
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, the sample means with size n of at least 30 can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
If 36 adults are randomly selected, find the probability that their mean body temperature is greater than 98.4degrees° F.
This is 1 subtracted by the pvalue of Z when X = 98.4. So
By the Central Limit Theorem
has a pvalue of 0.0228
1 - 0.0228 = 0.9772
97.72% probability that their mean body temperature is greater than 98.4degrees° F.