Utilizing the complement rule alongside the standard normal table or Excel, we arrive at the results.
To summarize previous concepts,
the normal distribution represents a symmetrical probability distribution centered around the mean, highlighting that values near the mean occur more frequently than those further away.
The Z-score acts as a statistical measure that indicates a value's relation to the average of a dataset, expressed in standard deviations from the mean.
In addressing the problem:
Let X denote the random variable representing population heights, and we regard the distribution for X as stipulated.
For a sample size of n = 64, since the distribution of X holds normality, so does the distribution of the sample mean.
We aim to determine the following probability, utilizing the Z-score derived via the specified formula.
Answer:
Attached is the histogram illustrating the marathon runners’ times.
Step-by-step explanation:
The provided data is as follows;
2.21
2.25
2.76
3.1
3.3
3.5
3.6
3.77
3.8
4.23
4.25
4.25
4.6
4.9
From this data, we can determine;
The count of runners finishing between 0 and 1 hour = 0
The count of runners finishing between 1 and 2 hours = 0
The count of runners finishing between 2 and 3 hours = 3
The count of runners finishing between 3 and 4 hours = 6
The count of runners finishing between 4 and 5 hours = 5
Based on these frequencies across the various time ranges, the histogram for the provided data has been constructed and is attached.
Answer:
Option (B)
Step-by-step explanation:
The given question is incomplete; please refer to the attached document for the full details.
In the attached graph,
The parent function is defined as an absolute value function,
f(x) = |x|
When this graph is moved four units to the left, the translation rule becomes,
f(x) → f(x + 4)
Consequently, the new function following this translation is,
g(x) = f(x + 4) = |x + 4|
Now, with the graph shifted down by two units, the translated function becomes,
h(x) = g(x) - 2
h(x) = |x + 4| - 2
When reformulated as an equation, the graph can be represented by
⇒ y = |x + 4| - 2
Thus, Option (B) is the correct answer.
<span>5.7 liters of a 5% solution combined with 4.3 liters of a 40% solution.
To begin, define the problem with formulas.
x Represents the liters of the 5% solution utilized.
10-x Represents the liters of the 40% solution used.
This forms an equation: 5% of x plus 40% of (10-x) equals 20% of 10.
0.05x + 0.40(10-x) = 0.20 * 10
Now, distribute the 0.40 coefficient.
0.05x + 4.0 - 0.40x = 0.20 * 10
Next, combine the terms.
4.0 - 0.35x = 2.0
Add 0.35x to each side.
4.0 = 2.0 + 0.35x
Subtract 2 from both sides.
2.0 = 0.35x
Lastly, divide both sides by 0.35.
5.7 = x
Thus, 5.7 liters of a 5% solution is required. To determine the volume of the 40% solution, subtract from 10.
10.0 - 5.7 = 4.3</span>
In the absence of a specific question posed, below are the potential inquiries along with their respective answers:
P(fewer than 4 tosses)
= P(one toss) + P(two tosses) + P(three tosses)
= (3/4) + (3/4)(1/4) + (3/4)(1/4)^2
= 0.984375
Expected value
= 1 / p
= 1 / (3/4)
= 4 / 3
Variance
= (1 - p) / p^2
= (1 - (3/4)) / (3/4)^2
= (1/4) / (9/16)
= 4 / 9
Standard deviation
= sqrt(Variance)
= sqrt(4 / 9)
= 2 / 3
