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2 answers:
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Answer:
In every 42 days, Sherman and Brad will go golfing on the same day.
Step-by-step explanation:
Given:
Sherman goes golfing every 6th day.
Brad goes golfing every 7th day.
If they both went golfing today, we need to determine how many days unit they will go golfing on the same day again.
Solution:
In order to determine how many days unit Sherman and Brad will go golfing on the same day again, we will take least common multiple of 6 and 7.
To find least common multiple of 6 and 7, we will list out their multiples.
We find out that the least common multiple of 6 and 7 =42.
Thus, we can conclude that Sherman and Brad will go golfing on same days on every 42nd day after they meet..
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