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
Svetradugi [14.3K]
3 years ago
11

Consider the probability that greater than 94 out of 153 people will not get the flu this winter. Assume the probability that a

given person will not get the flu this winter is 65%. Approximate the probability using the normal distribution. Round your answer to four decimal places.
Mathematics
1 answer:
Hatshy [7]3 years ago
7 0

Answer:

0.8212 = 82.12% probability that greater than 94 out of 153 people will not get the flu this winter.

Step-by-step explanation:

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:

p = 0.65, n = 153. So

\mu = E(X) = 153*0.65 = 99.45

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{153*0.65*0.35} = 5.9

Consider the probability that greater than 94 out of 153 people will not get the flu this winter

This probability is 1 subtracted by the pvalue of Z when X = 94. So

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

Z = \frac{94 - 99.45}{5.9}

Z = -0.92

Z = -0.92 has a pvalue of 0.1788

1 - 0.1788 = 0.8212

0.8212 = 82.12% probability that greater than 94 out of 153 people will not get the flu this winter.

You might be interested in
Help, will give brainliest :)
Alenkasestr [34]

Answer:

is c=b

Step-by-step explanation:

5 0
3 years ago
What are the x and y intercepts for -2x+y=-2​
SpyIntel [72]

Answer: The y intercepts would be: ( 0 , -2 ).

The x intercepts would be: ( 1 , 0 ).

Step-by-step explanation:

8 0
3 years ago
Consider the set of whole numbers from 3 to 30, inclusive.
Nadusha1986 [10]
2,4,6,8,10,12,14,16,18,20,22,24,26,28,30
8 0
3 years ago
Joseph traveled from Boston to Framingham at 50 mph and then back to Boston
Solnce55 [7]

Answer:

44.44 mph

Step-by-step explanation:

7 0
2 years ago
Blank divided by 7 is greater than 800
mrs_skeptik [129]
15,000 divided by 7 is greater than 800 but this question could have a number of possible answers
6 0
3 years ago
Read 2 more answers
Other questions:
  • Given the equation 10x + 20y + 40 = 0, Find it’s gradient and intercept
    6·1 answer
  • Write (-3, 5) and (-2, -6) standard form
    5·1 answer
  • What shape in this lesson can be used to prove statements about triangles?
    12·1 answer
  • PLEASE HELP ME! Thanks!
    13·1 answer
  • Jim Tree sells trees. The mean length of the trees purchased was 68 inches with a standard deviation of 10 inches. Jim wants to
    11·1 answer
  • Find three consecutive odd integers such that the sum of the smallest and twice the second is 14 more than the third.
    14·1 answer
  • Help! (math and area.) i'll give you brainliest!
    14·1 answer
  • How to solve 8-| 2(-3.5)-5 |
    15·1 answer
  • What would the answer be
    9·1 answer
  • Find the slope of a line perpendicular to each given line.<br><br> 7) y = 5/2x - 3
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!