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Jlenok [28]
4 years ago
15

Area unit conversion with whole numbers value 5 yards long and 4 wide = what in square feet?

Mathematics
1 answer:
Law Incorporation [45]4 years ago
4 0
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Southwest Co-op produces bags of fertilizer, and it is concerned about impurity content. It is believed that the weights of impu
Harman [31]

Answer:

a) 0.216

b) 0.1587

c) 0.369

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 12.2 grams

Standard Deviation, σ = 2.8 grams

We are given that the distribution of weights of impurities per bag is a bell shaped distribution that is a normal distribution.

Formula:

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

a) P(contains less than 10 grams of impurities)

P(x < 10)

P( x < 10) = P( z < \displaystyle\frac{10 - 12.2}{2.8}) = P(z < -0.7857)

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

P(x < 10) =0.216= 21.6\%

b) P(contains more than 15 grams of impurities)

P(x > 15)

P( x > 15) = P( z > \displaystyle\frac{15 - 12.2}{2.8}) = P(z > 1)

= 1 - P(z \leq 1)

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

P(x > 610) = 1 - 0.8413 = 0.1587 = 15.87\%

c) P(contains between 12 and 15 grams of impurities)

P(12 \leq x \leq 15) = P(\displaystyle\frac{12 - 12.2}{2.8} \leq z \leq \displaystyle\frac{15-12.2}{2.8}) \\\\= P(-0.0714 \leq z \leq 1)\\\\= P(z \leq 1) - P(z < -0.0714)\\= 0.841 - 0.472 = 0.369 = 36.9\%

P(12 \leq x \leq 15) = 36.9%

d) The mean divide the data in exactly two parts. Since 15 is farther away from the mean as compared to 10, the probability obtained in part (b) is smaller as compared to probability obtained in part (a).

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