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svlad2 [7]
2 years ago
11

In the United States, 75 percent of adults wear glasses or contact lenses. A random sample of 10 adults in the United States wil

l be selected.
What is closest to the probability that fewer than 8 of the selected adults wear glasses or contact lenses?
Mathematics
1 answer:
V125BC [204]2 years ago
4 0

Answer:

0.4745 is the probability that fewer than 8 of the selected adults wear glasses or contact lenses.

Step-by-step explanation:

We are given the following information:

We treat adult adults wear glasses or contact lenses as a success.

P(Adults wear glasses or contact lenses) = 75% = 0.75

Then the number of adults follows a binomial distribution, where

P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 10

We have to evaluate:

P(fewer than 8 of the selected adults wear glasses or contact lenses)

P(x < 8)\\=1 - P(x = 8) - P(x = 9) - P(x = 10)\\=1 - \binom{10}{8}(0.75)^8(1-0.75)^2 - \binom{10}{9}(0.75)^9(1-0.75)^1- \binom{10}{10}(0.75)^10(1-0.75)^0\\=1 - 0.2815-0.1877-0.0563\\= 0.4745

0.4745 is the probability that fewer than 8 of the selected adults wear glasses or contact lenses.

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On a coordinate plane, a piecewise function has 3 lines. The graph shows cleaning time in hours on the x-axis and total cost in
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Answer:

  C. (2, 6] hour jobs cost $100

Step-by-step explanation:

Let's consider each of these statements in view of the graph:

  1. A cleaning time of 2 hours will cost $100. -- The closed circle at (2, 50) tells you the cost of a 2-hour job is $50, not $100.
  2. A cleaning time of 6 hours will cost $150. -- The closed circle at (6, 100) tells you the cost of a 6-hour job is $100, not $150.
  3. Cost is a fixed rate of $100 for jobs requiring more than 2 hours, up to a maximum of 6 hours. -- The line between the open circle at (2, 100) and the closed circle at (6, 100) tells you this is TRUE.
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2 years ago
Write the ratio as a fraction in simplest form: 2.35 to 5.25.
Sliva [168]

Step-by-step explanation:

\frac{2.35}{5.25}  =  \frac{235}{525}  =  \frac{47}{105}  = 47 \:  : \: 105 \\

4 0
2 years ago
A consensus forecast is the average of a large number of individual analysts' forecasts. Suppose the individual forecasts for a
stealth61 [152]

Answer:

a) 0.954

b) 0.937

c) 0.891  

Step-by-step explanation:

We are given the following information in the question:

Mean, μ =  6 percent

Standard Deviation, σ = 1.3 percent

We are given that the distribution of particular interest rate is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

a) P(At least 3.8 percent.)

P(x \geq 3.8)

P( x \geq 3.8) = P( z \geq \displaystyle\frac{3.8 - 6}{1.3}) = P(z > -1.69)

= 1 - P(z < -1.69)

Calculation the value from standard normal z table, we have,  

P(x \geq 3.8) = 1 - 0.046 = 0.954 = 95.4\%

b) P(At most 8 percent)

P(x \leq 8) = P(z \leq \displaystyle\frac{8-6}{1.3}) = P(z \leq 1.53)

Calculating the value from the standard normal table we have,

P( x \leq 8) =0.937= 93.7\%

c) P(Between 3.8 percent and 8 percent. )

P(3.8 \leq x \leq 8) = P(-1.69 \leq z \leq 1.53)\\\\= P(z \leq 1.53) - P(z < -1.69)\\= 0.937 - 0.046 = 0.891 = 89.1\%

P(3.8 \leq x \leq 8) = 89.1\%

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2 years ago
Which point is a solution to the inequality shown in this graph?
Leviafan [203]

Answer:

A) (0,5)

Step-by-step explanation:

Coordinate point (0,5) lies within the bounded blue region

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No it will not be the same amount
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