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<h2>
Answer with explanation:</h2>
Confidence interval for mean, when population standard deviation is unknown:

, where
= sample mean
n= sample size
s= sample standard deviation
= Critical t-value for n-1 degrees of freedom
We assume the population has a normal distribution.
Given, n= 19 , s= 3.8 , 

A) Critical t value for
and degree of 18 freedom
= 2.8784
B) Required confidence interval:

Lower bound = 19.9 years
Uppen bound = 24.9 years
C) Interpretation: We are 99% confident that the true population mean of lies in (19.9, 24.9) .
Cheryl is 17 years old now.
Step-by-step explanation:
Let,
Age of Cheryl = x
Age of Henry = 2x+6
In 10 years;
Cheryl's age = x+10
Henry's age = 2x+6+10 = 2x+16
The sum of ages is 77.

Dividing both sides by 3

Age of Cheryl = 17 years
Age of Henry = 2x+6 = 2(17)+6 = 34+6 = 40 years
Cheryl is 17 years old now.
Keywords: variable, word problem
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