A small component for a machine is made from two metal spheres joined by a short metal bar. The mass

Question

A small component for a machine is made from two metal spheres joined by a short metal bar. The masses in grams of the spheres have the distribution $\mathrm{N}\left( 20,{{0.5}^{2}} \right)$. Find the probability that the mass of a randomly selected sphere is more than $20.2$ grams. [1] In order to protect them from rusting, the spheres are given a coating which increases the mass of each sphere by $10%$. Find the probability that the mass of a coated sphere is between $21.5$ and $22.45$ grams. State the distribution you use and its parameters. [3] The masses of the metal bars are normally distributed such that $60\%$ of them have a mass greater than $12.2$ grams and $25\%$ of them have a mass less than $12$ grams. Find the mean and standard deviation of the masses of metal bars. [4] The probability that the total mass of a component, consisting of two randomly chosen coated spheres and one randomly chosen bar, is more than $k$ grams is $0.75$. Find $k$, stating the parameters of any distribution you use. [4]

Accepted Answer

(i) 0.345, (ii) 0.612, (iii) μ=12.3g, σ=0.475g, (iv) k=55.7

N2017 P2 Q10

N2017 P2 Q10

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