The answers are A and B.
Hope this helps.
r3t40
Make x the subject of mx+a=nx-2 step by step answer please
2 answers:
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Answer:
68% of the rates are expected to be betwen 0.718 and 0.762
95% of the rates are expected to be betwen 0.696 and 0.784
99.7% of the rates are expected to be betwen 0.674 and 0.806
Step-by-step explanation:
Check for conditions
For this case in order to use the normal distribution for this case or the 68-95-99.7% rule we need to satisfy 3 conditions:
a) Independence : we assume that the random sample of 400 students each student is independent from the other.
b) 10% condition: We assume that the sample size on this case 400 is less than 10% of the real population size.
c) np= 400*0.74= 296>10
n(1-p) = 400*(1-0.74)=104>10
So then we have all the conditions satisfied.
Solution to the problem
For this case we know that the distribution for the population proportion is given by:
So then:
The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ). Broken down, the empirical rule shows that 68% falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).
68% of the rates are expected to be betwen 0.718 and 0.762
95% of the rates are expected to be betwen 0.696 and 0.784
99.7% of the rates are expected to be betwen 0.674 and 0.806
Answer:
And we can ue the z score formula given by:
And using this formula we got for the limits:
So we want to find this probability:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the annual income of a population, and for this case we know the following info:
and
and we are omitting the zeros from the thousand to simplify calculations
We select a sample size of n=50>30.
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
From the central limit theorem we know that the distribution for the sample mean is given by:
And we want to find this probability:
And we can ue the z score formula given by:
And using this formula we got for the limits:
So we want to find this probability: