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jumoke26
25.09.2021 •
Mathematics
After finishing her dental assistant program at a local technical college, Alex decided to transfer to a university to complete a dental hygiene program, her first paycheck as a dental hygienist is $3,200 before taxes. She works 490 hours per week, and worked 80 hours on her first paycheck. How much does Alex make per hour in her new job?
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Ответ:
Step-by-step explanation:
Given that:
p = 0.61
If X is the the number of students in a randomly selected group of a sample size n = 50
The expected value and the standard deviation can be computed as follows:
The expected value E(X) = np
The expected value E(X) = 50 × 0.61
The expected value E(X) = 30.5
The required standard deviation =![\sqrt{np(1-p)}](/tpl/images/0724/6189/53280.png)
The required standard deviation =![\sqrt{30.5(1-0.61)}](/tpl/images/0724/6189/2560b.png)
The required standard deviation =![\sqrt{30.5(0.39)}](/tpl/images/0724/6189/d9339.png)
The required standard deviation =![\sqrt{11.895}](/tpl/images/0724/6189/39de0.png)
The required standard deviation = 3.4489
The required standard deviation = 3.45
(b) Fill in the missing quantity. (Round your answer to the nearest whole number.)
There is an approximately 2.5% chance that _____ or more teenagers in the group will shop at the mall during the next week.
From the given information:
Now, we can deduce that:
the mean = 30.5
standard deviation = 3.45
Using the empirical rule:
At 95% confidence interval;
[μ - 2σ, μ + 2σ] = [ 30.5 - 2(3.45) , 30.5 + 2(3.45)]
[μ - 2σ, μ + 2σ] = [ 30.5 - 6.9 , 30.5 + 6.9]
[μ - 2σ, μ + 2σ] = [ 23.6, 37.4]
The 2.5% of the observations are less than 95% confidence interval and 2.5% observations are greater than 95% confidence interval.
The required number of teenagers is = the upper limit of the 95% confidence interval = 37
There is an approximately 2.5% chance that __37___ or more teenagers in the group will shop at the mall during the next week.