According to AccuData Media Research, 36% of televisions within the Chicago city limits are tuned to "Eyewitness News" at 5:00 p
1 answer:
Answer:
a) Mean: 900
Standard deviation: 24
b) Very unusual
c) Unusual
Step-by-step explanation:
We have a population proportion p=0.36 and we are taking a sample of size n=2500. This can be modeled as binomial sampling.
For this sampling distribution, we have a mean and STD that can be calculated as:
b) A value of 840 is a very unusual as is more than 2 standard deviations from the expected value of 900 (more exactly, at 2.5 standard deviations). Approximately 2% of the values are below 2 standars deviations from the mean.
Having 840 or less televisions tuned to "Eyewitness News" would have a probability of P=0.00621.
c) A value of 945 would be also unusual, but not as unusual as 840, as is between 1 and 2 standard deviation from the expected value.
Having 945 or more televisions tuned to "Eyewitness News" would have a probability of P=0.0304.
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Answer:
a) By the Central Limit Theorem, the distribution would be approximately normal, with mean and standard deviation
b) 4.02 standard deviations below the mean.
c) Making 25 or less shots has a pvalue of -4.02. Z-scores lower than -2 are considered surprising, so yes, it would be surprising for him to make only 25 of these shots.
Step-by-step explanation:
To solve this question, we are going to 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.
For proportions, we have that the mean is and the standard deviation is
In this problem, we have that:
a)By the Central Limit Theorem, the distribution would be approximately normal, with mean and standard deviation
b)This is Z when X = 0.25.
By the Central Limit Theorem
4.02 standard deviations below the mean.
c) Making 25 or less shots has a pvalue of -4.02. Z-scores lower than -2 are considered
surprising, so yes, it would be surprising for him to make only 25 of these shots.
Answer:
I guess that You made a mistake and You wanted to solve equations . Then the answer is D because There is no number that gives a negative number after the square root
Step-by-step explanation: