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Answer:
0% probability that the sample mean would have been as high or higher than 3.1 if the company’s claims were true.
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 random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
What is the approximate probability that the sample mean would have been as high or higher than 3.1 if the company’s claims were true?
This is 1 subtracted by the pvalue of Z when X = 3.1. So
By the Central Limit Theorem
has a pvalue of 1.
1 - 1 = 0
0% probability that the sample mean would have been as high or higher than 3.1 if the company’s claims were true.
The missing part of the question is show in bold format.
Your teacher gives you a number cube with numbers 1-6 on its faces. You are asked to state a theoretical probability model for rolling it
once. Your probability model shows a probable outcome of 1/6 for each of the numbers on the cube, 1 chance for all any of the 6 numbers.
You roll it 500 times and get the following data:
Outcome 1 2 3 4 5 6
Frequency 77 92 75 90 76 90
Exercises 1–2
1. If the equality model was correct, about how many of each outcome
would you expect to see if the cube is rolled 500 times
2. Based on the data from the 500 rolls, how often were odd numbers observed? How often were even numbers observed?
Answer:
Step-by-step explanation:
1.
If the equally likely model was correct, about how many of each outcome
would you expect to see if the cube is rolled 500 times.
The probability of rolling any of the numbers from 1 to 6 is p(1/6)
The number of each of the outcomes expected to be seen in 500 rolls of the number cube is
2. From the given data in the roll;
The odd numbers 1, 3 and 5, were obtained at 77, 75 and 76 times respectively.
Thus, the total number of times odd number were rolled = 77 + 75 + 76 = 228
Probability of an odd number turning up =
=
= 0.456
= 45.6%
The even numbers, 2, 4 and 6, were obtained 92, 90 and 90 times respectively.
The total number of times even number were rolled = 92 + 90 + 90 = 272
Probability of an even number turning up =
=
= 0.544
= 54.4%