The rock band, Screamin’ Meanies, has a fan club that publishes a monthly newsletter. Expenses are $.35 for printing and mailing
2 answers:
Answer: There are 3850 copies of the newsletter that must the club sell to break even each month.
Step-by-step explanation:
Let the number of copies of the newsletter be 'x'.
Cost of printing and mailing each = $0.35
Total cost for research, writing and other costs = $770
Total cost price would be
Cost of the newspaper each copy = $0.55
Total selling price would be
So, the break even point would be
Total cost price = Total selling price
Hence, there are 3850 copies of the newsletter that must the club sell to break even each month.
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Answer:
0.2460 = 24.60% probability that the mean weight of the sample of cows would differ from the population mean by more than 11 lbs if 116 cows are sampled at random from the herd.
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(which is the square root of the variance)
, 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 mean weight of the sample of cows would differ from the population mean by more than 11 lbs if 116 cows are sampled at random from the herd?
This is 2 multiplied by the pvalue of Z when X = 1217 - 11 = 1206. So
By the Central Limit Theorem
has a pvalue of 0.1230
2*0.1230 = 0.2460
0.2460 = 24.60% probability that the mean weight of the sample of cows would differ from the population mean by more than 11 lbs if 116 cows are sampled at random from the herd.