Pepper Jackie has 7.5 bags of mulch to cover 12 yds squared 2 of edible flower beds. If she wants to distribute the mulch evenly
2 answers:
Answer:
Step-by-step explanation:
Data provided in the question
Number of bags of mulch = 7.5 bags
Number of square yards = 12
So by considering above information, we could find the number of bags for each square yard is
=
=
= 0.625
The 0.625 is equal to bag
Therefore, she need to use bag for each square yard
Basically we use the fraction so that each square yard for use of bag could be find out
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Answer:
a) 0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.
b) 0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use 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 question, we have that:
a. What is the probability that the sample mean will be within +/- 5 of the population mean (to 4 decimals)?
This is the pvalue of Z when X = 200 + 5 = 205 subtracted by the pvalue of Z when X = 200 - 5 = 195.
Due to the Central Limit Theorem, Z is:
X = 205
has a pvalue of 0.8413.
X = 195
has a pvalue of 0.1587.
0.8413 - 0.1587 = 0.6426
0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.
b. What is the probability that the sample mean will be within +/- 10 of the population mean (to 4 decimals)?
This is the pvalue of Z when X = 210 subtracted by the pvalue of Z when X = 190.
X = 210
has a pvalue of 0.9772.
X = 195
has a pvalue of 0.0228.
0.9772 - 0.0228 = 0.9544
0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.