1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Nookie1986 [14]
3 years ago
12

20% of US High School teens vape. A local High School has implemented campaigns to reduce vaping among students and believes tha

t the percentage of students who vape at this High School is lower than the national average. School administration implements a survey of 300 randomly selected students. They find that 51 of the 300 vape.
If the true proportion of students who vape at this school is 20%, what is the approximate probability of observing 51 or fewer vapers in a random sample of 300?
Mathematics
1 answer:
zaharov [31]3 years ago
4 0

Answer:

10.93% probability of observing 51 or fewer vapers in a random sample of 300

Step-by-step explanation:

I am going to use the normal approximation to the binomial to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

n = 300, p = 0.2

So

\mu = E(X) = np = 300*0.2 = 60

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{300*0.2*0.8} = 6.9282

What is the approximate probability of observing 51 or fewer vapers in a random sample of 300?

Using continuity corrections, this is P(X \leq 51 + 0.5) = P(X \leq 51.5), which is the pvalue of Z when X = 51.5 So

Z = \frac{X - \mu}{\sigma}

Z = \frac{51.5 - 60}{6.9282}

Z = -1.23

Z = -1.23 has a pvalue of 0.1093.

10.93% probability of observing 51 or fewer vapers in a random sample of 300

You might be interested in
Britney bought 2 apples, 5 bananas, and 8 oranges at the grocery store.
Sladkaya [172]

Answer:

2 apples: 5 bananas: 8 oranges

Final answer: 1 apple: 2,5 bananas ( divide by 2 )

5 0
3 years ago
Read 2 more answers
A family drove 1 /5 of the total distance to the coast on the first day. They drove another2/5 of the distance on the second day
ser-zykov [4K]
1/5+2/5=3/5 answer C
5 0
3 years ago
Which of the following is a good way to quickly determine whether 3/12 and 1/4 are equal​
Novay_Z [31]

Answer: Divide 3 into the numerator and denominator

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
A skateboarder starting from rest accelerates down a ramp at 2 m/s for 2 s. What is the final speed of the skateboarder
Sedaia [141]

Initial speed of the skateboard (u) = 0 m/s (Starts from rest)

Acceleration of the skateboard (a) = 2 m/s²

Time taken by the skateboard (t) = 2s

By using equation of motion, we get:

\bf \longrightarrow v = u + at \\  \\ \rm \longrightarrow v = 0 + 2 \times 2 \\  \\ \rm \longrightarrow v = 4 \: m {s}^{ - 1}

\therefore Final speed of the skateboard(v) = 4 m/s

7 0
3 years ago
PLEASE HELP. IF U GET THIS RIGHT I WILL MARK U BRAINLIEST!!! THANK U GUYS
KatRina [158]

Answer:

2

Step-by-step explanation:

The slope is the rise over the run. 2 simple coordinates I can see is (6,2) and (7,4). I usually like to visualize it instead of actually solving it mathematically. So, we can start at (6,2). The point (6,2) goes up 2 and 1 to the right in order to get (7,4.) So since the slope is rise over run ( y/x) it would be 2/1 because we went 2 up the y axis and 1 to the right of the x axis. So 2/1 is 2. Therefore, 2 is the answer.  I'm sorry if my explaining isn't the best... I hope this helps though!!

6 0
3 years ago
Other questions:
  • create a problem about the estimated cost of ingredients for the recipe if onion cost 2.99 stats lb and pork cost $5.49 lb. incl
    5·1 answer
  • Rounding 0.912 to the nearest hundredth
    15·2 answers
  • What is payments of $3,920.00 in three installments
    7·1 answer
  • (7x – 2y) – (3x + 5y)
    11·2 answers
  • For which value of X is the row in the table of values incorrect? The function is the quadratic function Y=3/4x^2
    8·1 answer
  • What is the greatest common factor of 15n^5, 30n^3, and 45n^2?
    11·2 answers
  • What is the answer for 1-2...please show how you got the answer....thank you
    12·1 answer
  • B-4/6=b/2. Solve for b.
    12·1 answer
  • Make sure and read this carefully!
    10·2 answers
  • Evaluate the expression if x = 3 and y = 11. 3x + 2y 21 31 42 244
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!