The random variable $X$ has the distribution $\mathrm{N}\left( a,b \right)$, where $a$ and $b$ are p

Question

The random variable $X$ has the distribution $\mathrm{N}\left( a,b \right)$, where $a$ and $b$ are positive real numbers. It is also given that $\mathrm{P}\left( X\le 45 \right)=0.5$ and $\mathrm{P}\left( 45 State the value of $a$ and show that $b=2273$, correct to the nearest integer. [3] In this part of the question you should state clearly the values of the parameters of any normal distribution you use. The masses in grams of bananas have the distribution $\mathrm{N}\left( 180,\mathrm{ }200 \right)$and the masses in grams of mangoes have the distribution $\mathrm{N}\left( 150,\mathrm{ }225 \right)$. Find the probability that the total mass of $3$ randomly chosen bananas is between $520$ and $650$ grams. [2] Find the probability that the total mass of $4$ bananas is more than $5$ times the mass of a mango. [3] State an assumption needed for your calculations in part (b)(ii). [1]

Accepted Answer

(a) $a=45$, $b=2273$; (b)(i) $0.793$; (b)(ii) $0.354$

2022 NJC J2 CT P2 Q3

2022 NJC J2 CT P2 Q3

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