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st3ph
16.07.2019 •
Mathematics
What is negative twenty times three? −20 ⋅ 3
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Ответ:
Ответ:
20×3=60
since its a negative, just add the sign
-60
Ответ:
0.8996 = 89.96% probability that the sample proportion will be between 0.2 and 0.4
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 normal distributions can be solved using the z-score formula.
In a set with mean
and standard deviation
, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes 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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean
and standard deviation ![s = \sqrt{\frac{p(1-p)}{n}}](/tpl/images/1387/4985/73804.png)
The manager of a donut store believes that 35% of the customers are first-time customers.
This means that![p = 0.35](/tpl/images/1387/4985/446bd.png)
Sample of 150 customers
This means that![n = 150](/tpl/images/1387/4985/3f95d.png)
Mean and standard deviation:
What is the probability that the sample proportion will be between 0.2 and 0.4?
p-value of Z when X = 0.4 subtracted by the p-value of Z when X = 0.2.
X = 0.4
By the Central Limit Theorem
X = 0.2
0.8997 - 0.0001 = 0.8996
0.8996 = 89.96% probability that the sample proportion will be between 0.2 and 0.4