Given a population with a mean of muμequals=100100 and a variance of sigma squaredσ2equals=3636, the central limit theorem appl
1 answer:
Answer:
a)
b)
c)
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".
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".
The complement rule is a theorem that provides a connection between the probability of an event and the probability of the complement of the event. Lat A the event of interest and A' the complement. The rule is defined by:
Let X the random variable that represent the variable of interest on this case, and for this case we know the distribution for X is given by:
And let represent the sample mean, by the central limit theorem, the distribution for the sample mean is given by:
a. What are the mean and variance of the sampling distribution for the sample means?
b. What is the probability that x overbarxgreater than>101
First we can to find the z score for the value of 101. And in order to do this we need to apply the formula for the z score given by:
If we apply this formula to our probability we got this:
And we want to find this probability:
On this last step we use the complement rule.
c. What is the probability that x bar 98less than
First we can to find the z score for the value of 98.
And we want to find this probability:
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Answer:
Check the explanation
Step-by-step explanation:
Here we have to first of all carry out dependent sample t test. consequently wore goggles first was selected at random for the reason that the reaction time in an emergency taken with goggles would be greater than the amount of reaction time in an emergency taken with not so weakened vision. So that we will get the positive differences d = impaired - normal
b)
To find 95% confidence interval first we need to find sample mean and sample sd for difference d = impaired minus normal.
We can find it using excel that is in the first attached image below,
Therefore sample mean = 0.98
Sample sd = 0.3788
To find 95% Confidence interval we can use TI-84 calculator,
Press STAT ----> Scroll to TESTS ---- > Scroll down to 8: T Interval and hit enter.
Kindly check the attached image below.
Therefore we are 95% confident that mean difference in braking time with impaired vision and normal vision is between ( 0.6888 , 1.2712)
Conclusion : As both values in the interval are greater than 0 , mean difference impaired minus normal is not equal to 0
There is significant evidence that there is a difference in braking time with impaired vision and normal vision at 95% confidence level .
Answer:
A linear function is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
An exponential equation is written as:
y = A*(r)^x
Where A is the initial quantity and r is the rate of growth.
If a and A are both positives, the similar characteristic of both types of functions is that as x increases, then the value of y will also increase. Then both functions are increasing functions.
They are different in how they increase, while a linear function increases at a constant rate, an exponential function increases slow at the beginning and really fast as x increases, as you can see in the image below where we compare the two types of functions, the green one is the linear function, and the blue one is the exponential function.
