Answer:
Step-by-step explanation:
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The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 247.9 and a standard deviation of
64.7. (All units are 1000 cells/μL.) Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of women with platelet counts within 2 standard deviations of the mean, or between 118.5 and 377.3? b. What is the approximate percentage of women with platelet counts between 53.8 and 442.0?
1 answer:
Answer:
A) Approximate percentage of women with platelet counts within 2 standard deviations of the mean, or between 118.5 and 377.3 = 95%
B) approximate percentage of women with platelet counts between 53.8 and 442.0 = 99.7%
Step-by-step explanation:
We are given;
mean;μ = 247.9
standard deviation;σ = 64.7
A) We want to find the approximate percentage of women with platelet counts within 2 standard deviations of the mean, or between 118.5 and 377.3.
Now, from the image attached, we can see that from the empirical curve, the probability of 1 standard deviation from the mean is (34% + 34%) = 68 %.
While probability of 2 standard deviations from the mean is (13.5% + 34% + 34% + 13.5%) = 95%
Thus, approximate percentage of women with platelet counts within 2 standard deviations of the mean, or between 118.5 and 377.3 = 95%
B) Now, we want to find the approximate percentage of women with platelet counts between 53.8 and 442.0.
53.8 and 442.0 represents 3 standard deviations from the mean.
Let's confirm that.
Since mean;μ = 247.9
standard deviation;σ = 64.7 ;
μ = 247.9
σ = 64.7
μ + 3σ = 247.9 + 3(64.7) = 442
Also;
μ - 3σ = 247.9 - 3(64.7) = 53.8
Again from the empirical curve attached, we cans that at 3 standard deviations from the mean, we have a percentage probability of;
(2.35% + 13.5% + 34% + 34% + 13.5% + 2.35%) = 99.7%
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Answer:
a) represent the real population proportion of people who showed partial or complete resistance to the antibiotic
b) represent the estimated proportion of people who showed partial or complete resistance to the antibiotic
c) We are confident (95%) that the true proportion of individuals in Florida diagnosed with a strep infection was tested for resistance to the antibiotic penicillin present partial or complete resistance to the antibiotic is between 54.5% to 59.1%.
Step-by-step explanation:
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
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".
Part a
Description in words of the parameter p
represent the real population proportion of people who showed partial or complete resistance to the antibiotic
represent the estimated proportion of people who showed partial or complete resistance to the antibiotic
n=1714 is the sample size required
represent the critical value for the margin of error
The population proportion have the following distribution
Part b
Numerical estimate for p
In order to estimate a proportion we use this formula:
where X represent the number of people with a characteristic and n the total sample size selected.
represent the estimated proportion of people who showed partial or complete resistance to the antibiotic
Part c
The confidence interval for a proportion is given by this formula
For the 95% confidence interval the value of and
, with that value we can find the quantile required for the interval in the normal standard distribution.
And replacing into the confidence interval formula we got:
And the 95% confidence interval would be given (0.545;0.591).
We are confident that about 54.5% to 59.1% of individuals in Florida diagnosed with a strep infection was tested for resistance to the antibiotic penicillin present partial or complete resistance to the antibiotic.