Ling wants to determine the average distance she travels each day in her car. She records the odometer reading, which measures t
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Answer:
And we can solve this using the following z score formula:
And if we use this formula we got:
So we can find this probability equivalently like this:
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 heights of a population, and for this case we know the distribution for X is given by:
Where and
We select n =100. Since the distribution for X is normal then we know that the distribution for the sample mean is given by:
We want this probability:
And we can solve this using the following z score formula:
And if we use this formula we got:
So we can find this probability equivalently like this:
Answer:
95% confidence interval for the proportion of the population which are on treatment is [0.3293 , 0.3607].
Step-by-step explanation:
We are given that during the 7th examination of the Offspring cohort in the Framing ham Heart Study, there were 1219 participants being treated for hypertension and 2,313 who were not on treatment.
The sample proportion is : = x/n = 1219/3532 = 0.345
Firstly, the pivotal quantity for 95% confidence interval for the proportion of the population is given by;
P.Q. = ~ N(0,1)
where, = sample proportion = 0.345
n = sample of participants = 3532
p = population proportion
<em>Here for constructing 95% confidence interval we have used One-sample z proportion statistics.</em>
So, 95% confidence interval for the population proportion, p is ;
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level of
significance are -1.96 & 1.96}
P(-1.96 < < 1.96) = 0.95
P( <
<
) = 0.95
P( < p <
) = 0.95
<u>95% confidence interval for p</u>= [ ,
]
= [ ,
]
= [0.3293 , 0.3607]
Hence, 95% confidence interval for the proportion of the population which are on treatment is [0.3293 , 0.3607].