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
Leni [432]
2 years ago
5

Suppose it is known that 60% of radio listeners at a particular college are smokers. A sample of 500 students from the college i

s selected at random. Approximate the probability that at least 280 of these students are radio listeners.
Mathematics
1 answer:
vladimir1956 [14]2 years ago
8 0

Answer:

The probability that at least 280 of these students are smokers is 0.9664.

Step-by-step explanation:

Let the random variable <em>X</em> be defined as the number of students at a particular college who are smokers

The random variable <em>X</em> follows a Binomial distribution with parameters n = 500 and p = 0.60.

But the sample selected is too large and the probability of success is close to 0.50.

So a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:

1. np ≥ 10

2. n(1 - p) ≥ 10

Check the conditions as follows:

 np=500\times 0.60=300>10\\n(1-p)=500\times(1-0.60)=200>10

Thus, a Normal approximation to binomial can be applied.

So,  

X\sim N(\mu=600, \sigma=\sqrt{120})

Compute the probability that at least 280 of these students are smokers as follows:

Apply continuity correction:

P (X ≥ 280) = P (X > 280 + 0.50)

                   = P (X > 280.50)

                   =P(\frac{X-\mu}{\sigma}>\frac{280-300}{\sqrt{120}}\\=P(Z>-1.83)\\=P(Z

*Use a <em>z</em>-table for the probability.

Thus, the probability that at least 280 of these students are smokers is 0.9664.

You might be interested in
Which ordered pairs are solutions to the inequality y−4x≤−6 ?
Darina [25.2K]

Answer: y-4x > -6

Step-by-step explanation: Y-4x is 4x is positive and if you are above the Zero on a negative and positive chart the positives are always higher then the negatives.

5 0
3 years ago
I don't know how to do these<br>need help​
elena-s [515]

Answer:

spinner 2 is 14

Step-by-step explanation:

7+3=10

10+4=13

8 0
2 years ago
I WILL MARK BRAINLIEST
zaharov [31]

Answer:

y - 6 = - 3(x + 1)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = - 3 and (a, b) = (- 1, 6) , then

y - 6 = - 3(x - (- 1) ) , that is

y - 6 = - 3(x + 1)

7 0
2 years ago
Read 2 more answers
Noah picked 3 kilograms of cherries. Mai picked half as many cherries as Noah. How many total kilograms of cherries die Mia and
Angelina_Jolie [31]

it would be 4.5 total

6 0
3 years ago
Which graph represents the solution of y &gt; x2 + 2?
Vladimir [108]
The questions is asking which one and i say is graph B
4 0
1 year ago
Read 2 more answers
Other questions:
  • 1+123457890134875986​
    15·1 answer
  • What is the 3rd term of the sequence? <br> a1 = 40 and an = 0.5(an – 1) <br> a3 =
    8·1 answer
  • Find the slope of the line through each pair of points.
    5·1 answer
  • A community center is offering a discount on
    11·2 answers
  • Find variable c:<br><br><br> -65c = -5
    11·1 answer
  • Can you think of any other real-life scenarios where parallel lines and transversals<br> exist ?
    11·2 answers
  • Which measurement is not equal 51 centimeters
    13·2 answers
  • What 2d shapes make a cylinder
    10·1 answer
  • Find the product of quotient using only positive exponents
    5·1 answer
  • There are 60 students in a class. Girls make up 20% of the class and 45% of them have phones. How many girls in the class have p
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!