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Sergio [31]
2 years ago
5

A total of 150 students have taken an Algebra 2 final exam. The scores are normally distributed with a mean of 71% and standard

deviation of 6%. How many students would you expect have scored between 65% and 77%?
Mathematics
1 answer:
WARRIOR [948]2 years ago
3 0

Answer:

102 students

Step-by-step explanation:

Note that 65% and 71% are both 1 standard deviation from the mean (71%).  According to the empirical rule, 68% of scores lie within 1 std. dev. of the mean.

68% of 150 students would be 0.68(150 students) = 102 students

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a certain pharmaceutical company know that, on average 4% of a certain type of pill has an ingredient that is below the minimum
FinnZ [79.3K]

Using the binomial distribution, it is found that there is a 0% probability that fewer that 5 in a sample of 20 pills will be acceptable.

For each pill, there are only two possible outcomes, either it is acceptable, or it is not. The probability of a pill being acceptable is independent of any other pill, which means that the binomial distribution is used to solve this question.

Binomial probability distribution

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

C_{n,x} = \frac{n!}{x!(n-x)!}

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.

In this problem:

  • The sample has 20 pills, hence n = 20.
  • 100 - 4 = 96% are acceptable, hence p = 0.96

The probability that <u>fewer that 5 in a sample of 20 pills</u> will be acceptable is:

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

In which

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{20,0}.(0.96)^{0}.(0.04)^{20} = 0

P(X = 1) = C_{20,1}.(0.96)^{1}.(0.04)^{19} = 0

P(X = 2) = C_{20,2}.(0.96)^{2}.(0.04)^{18} = 0

P(X = 3) = C_{20,3}.(0.96)^{3}.(0.04)^{17} = 0

P(X = 4) = C_{20,4}.(0.96)^{4}.(0.04)^{16} = 0

0% probability that fewer that 5 in a sample of 20 pills will be acceptable.

A similar problem is given at brainly.com/question/24863377

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Answer:

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George is helping the manager of the local produce market expand her business by distributing flyers
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Answer:

20 + 0.05x ≥ 65

Step-by-step explanation:

20 is by itself since thats what he earns extra per day.

Since he earns 0.05 per flyer, that means we are going to need a variable since we don't know how many flyers he passes. Let x be equal to that.

Since he wants to make at LEAST 65 we are going to use the greater than or equal to symbol since he doesn't want to make less than that.

20 + 0.05x ≥ 65

Best of Luck!

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Answer:

y= 1/3x

Step-by-step explanation:

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(0,0), (3,1)

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y= 1/3x

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