On Saturday, there were seven people chosen at random to fill out a survey about how much time they spend each week on the tread
mill. Their survey results are shown below on the data table. Use the table to compute the average amount of time spent on the treadmill on Thursday this week. Type a numerical answer in the space provided. If there is more than one answer, use a comma to separate your answers.
1 answer:
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Using the binomial distribution, it is found that:
a) There is a 0.1618 = 16.18% probability that among 18 randomly observed individuals exactly 6 do not cover their mouth when sneezing.
b) There is a 0.104 = 10.4% probability that among 18 randomly observed individuals fewer than 3 do not cover their mouth when sneezing.
c) 9 is more than 2.5 standard deviations below the mean, hence it would not be surprising if fewer than half covered their mouth when sneezing.
<h3>What is the binomial distribution formula?</h3>The formula is:
The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
The values of the parameters are given as follows:
n = 18, p = 0.267.
Item a:
The probability is P(X = 6), hence:
There is a 0.1618 = 16.18% probability that among 18 randomly observed individuals exactly 6 do not cover their mouth when sneezing.
Item b:
The probability is:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2).
Then:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0037 + 0.0245 + 0.0758 = 0.104.
There is a 0.104 = 10.4% probability that among 18 randomly observed individuals fewer than 3 do not cover their mouth when sneezing.
item c:
We have to look at the mean and the standard deviation, given, respectively, by:
- E(X) = np = 18 x 0.267 = 4.81.
9 is more than 2.5 standard deviations below the mean, hence it would not be surprising if fewer than half covered their mouth when sneezing.
More can be learned about the binomial distribution at brainly.com/question/24863377
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