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2 years ago

Question 9 (3 points)

Mathematics

1 answer:

Mila [183]2 years ago

5 0

From the dot plot, we have that 90.91% of the students have 5 or more vowels in their first and last names.

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The dot plot states that:

2 students have 4 vowels in their first and last name.
3 students have 5 vowels.
8 students have 6 vowels.
9 students have 7 vowels.

Then:

Total of 2 + 3 + 8 + 9 = 22 students.
3 + 8 + 9 = 20 have or more vowels.

$p = \frac{20}{22} \times 100\% = 90.91\%$

90.91% of the students have 5 or more vowels in their first and last names.

A similar problem is given at brainly.com/question/14354536

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Suppose X is the breaking strength (newtons) of a material, and X is normally distributed with

Veronika [31]

Answer:

a) 0.997 is the probability that the breaking strength is at least 772 newtons.

b) 0.974 is the probability that this material has a breaking strength of at least 772 but not more than 820

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 800 newtons

Standard Deviation, σ = 10 newtons

We are given that the distribution of breaking strength is a bell shaped distribution that is a normal distribution.

Formula:

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

a) P( breaking strength of at least 772 newtons)

$P(x \geq 772)$

$P( x \geq 772) = P( z \geq \displaystyle\frac{772 - 800}{10}) = P(z \geq -2.8)$

$= 1 - P(z$

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

$P(x \geq 772) = 1 - 0.003 = 0.997 = 99.7\%$

0.997 is the probability that the breaking strength is at least 772 newtons.

b) P( breaking strength of at least 772 but not more than 820)

$P(772 \leq x \leq 820) = P(\displaystyle\frac{772 - 800}{10} \leq z \leq \displaystyle\frac{820-800}{10}) = P(-2.8 \leq z \leq 2)\\\\= P(z \leq 2) - P(z < -2.8)\\= 0.977 - 0.003 = 0.974 = 97.4\%$

$P(772 \leq x \leq 820) = 97.4\\%$

0.974 is the probability that this material has a breaking strength of at least 772 but not more than 820.

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