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2 months ago

In a small private school three students are randomly selected from 18 available students what is the probability that

Mathematics

1 answer:

tester [12.3K]2 months ago

3 0

1/ 816

Step-by-step explanation:

Step 1 :

Assumptions made

Number of students in the school = 18

Number selected randomly = 3

Step 2 :

Calculating number of ways to choose 3 students from a group of 18:

C(18,3) = 18! /(3!(18-3)!) = 18*17*16/3*2*1 = 816

Ways to choose the youngest 3 students = 1

Hence, the probability of picking the 3 youngest students from this group is 1/ C(18,3) = 1/ 816

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The weights of certain machine components are normally distributed with a mean of 8.01 g and a standard deviation of 0.06 g. Fin

PIT_PIT [12445]

Answer:

Option D) 7.90 g and 8.12 g

Step-by-step explanation:

The details provided in the question are:

Mean, μ = 8.01 g

Standard Deviation, σ = 0.06 g

The weights are distributed in a bell-shaped normal distribution.

Formula:

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

We need to determine the value of x for which the probability is 0.03.

P(X > x)

$P( X > x) = P( z > \displaystyle\frac{x - 8.01}{0.06})=0.03$

$= 1 -P( z \leq \displaystyle\frac{x - 8.01}{0.06})=0.03$

$=P( z \leq \displaystyle\frac{x - 8.01}{0.06})=0.97$

Using the standard normal z table, we find that,

$\displaystyle\frac{x - 8.01}{0.06} = 1.881\\\\x = 8.12$

Thus, the value of 8.17 g separates the upper 3% of the weights.

P(X < x)

$P( X < x) = P( z < \displaystyle\frac{x - 8.01}{0.06})=0.03$

From the standard normal z table, we derive,

$\displaystyle\frac{x - 8.01}{0.06} = -1.881\\\\x = 7.90$

Consequently, 7.90 separates the lower 3% of the weights.

Option D) 7.90 g and 8.12 g

</ptherefore>

7 0

1 month ago

Solve the equation. y + 6 = –3y + 26 y = –8 y = –5 y = 5 y = 8

zzz [12365]

In this situation, we start with the following equation: To isolate the value of y, we follow these steps: First, we subtract 6 from both sides of the equation: Second, we take away "y" from each side: Third, we add $4y$ to both sides of the equation: Finally, we divide the equation by 4. Thus, y equals 5. Answer: Option C.