Answer:
A. length = 23 cm; width = 5 cm
Step-by-step explanation:
So if 4 times the width would be and 3 more than would be
, the equation would be
. If the perimeter is 56, then the new equation,
can be formed. This simplifies to
, then to
, then to
, and finally,
. So the width is 5, and now plug it into the first equation.
, becomes
, becomes
.
So the dimensions are: length = 23 cm, width = 5 cm.
*And just to be sure, which is correct.
Answer:
b. Mean = 1.6 years, standard deviation - 0.92 years, shape: approximately Normal.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction of normal Variables:
When we subtract normal variables, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.
A consumer group has determined that the distribution of life spans for gas ranges (stoves) has a mean of 15.0 years and a standard deviation of 4.2 years. Sample of 35:
This means that:
The distribution of life spans for electric ranges has a mean of 13.4 years and a standard deviation of 3.7 years. Sample of 40:
This means that:
Which of the following best describes the sampling distribution of the difference in mean life span of gas ranges and electric ranges?
Shape is approximately normal.
Mean:
Standard deviation:
So the correct answer is given by option b.