Given:
n = 20, sample size
xbar = 17.5, sample mean
s = 3.8, sample standard deiation
99% confidence interval
The degrees of freedom is
df = n-1 = 19
We do not know the population standard deviation, so we should determine t* that corresponds to df = 19.
From a one-tailed distribution, 99% CI means using a p-value of 0.005.
Obtain
t* = 2.8609.
The 99% confidence interval is
xbar +/- t*(s/√n)
t*(s/√n) = 2.8609*(3.8/√20) = 2.4309
The 99% confidence interval is
(17.5 - 2.4309, 17.5 + 2.4309) = (15.069, 19.931)
Answer: The 99% confidence interval is (15.07, 19.93)
The value of the expression is 256
Answer:
The constant of proportionality is option D i.e 5.
Step-by-step explanation:
Variation:
Variation problems involve fairly simple relationships or formulas, involving one variable being equal to one term. There are two types of variation i.e.
- Direct variation
- Inverse variation
Direct Variation:
Mathematical relationship between two variables that can be expressed by an equation in which one variable is equal to a constant times the other.
Example 
where, k is constant of proportionality.
The above given example is of Direct Variation
∴ y = 5 x
∴ k = 5 = constant of proportionality.
Inverse Variation:
Mathematical relationship between two variables which can be expressed by an equation in which the product of two variables is equal to a constant.
Example 
where, k is constant of proportionality.