A mandatory competency test high school morphemes has a normal distribution with

Question

A mandatory competency test high school morphemes has a normal distribution with a mean of 1660 and a deviations of 120. The top 3% of the students receive $900. What is the minimum score you would need so win reward? Use Confidence intervals to estimate the true population mean. (Label curves - optional) A sample of 50 people who play the lottery found the mean amount of money that people spend to be $23.50 and the standard deviation of the population is 3. Find the 95% confidence interval of the population mean.

Explanation / Answer

Q10.

Confidence Interval
CI = x ± Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=23.5
Standard deviation( sd )=3
Sample Size(n)=50
Confidence Interval = [ 23.5 ± Z a/2 ( 3/ Sqrt ( 50) ) ]
= [ 23.5 - 1.96 * (0.42) , 23.5 + 1.96 * (0.42) ]
= [ 22.67,24.33 ]
Interpretations:
1) We are 95% sure that the interval [22.67 , 24.33 ] contains the true population mean
2) If a large number of samples are collected, and a confidence interval is created
for each sample, 95% of these intervals will contains the true population mean  

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