We study the production of a factory that manufactures sweets, packaged in bags. A bag is chosen at random from daily production. The mass of this bag, expressed in grams, is modelled by a random variable $X$ which follows a normal distribution with mean $\mu = 175$. Furthermore, statistical observation has shown that $2\%$ of bags have a mass less than or equal to 170 g, which is expressed in the model considered by: $P ( X \leqslant 170 ) = 0.02$. What is the probability, rounded to the nearest hundredth, of the event ``the mass of the bag is between 170 and 180 grams''? Answer a: 0.04 Answer b: 0.96 Answer c: 0.98 Answer d: We cannot answer because data is missing.
We study the production of a factory that manufactures sweets, packaged in bags. A bag is chosen at random from daily production. The mass of this bag, expressed in grams, is modelled by a random variable $X$ which follows a normal distribution with mean $\mu = 175$. Furthermore, statistical observation has shown that $2\%$ of bags have a mass less than or equal to 170 g, which is expressed in the model considered by: $P ( X \leqslant 170 ) = 0.02$.
What is the probability, rounded to the nearest hundredth, of the event ``the mass of the bag is between 170 and 180 grams''?
Answer a: 0.04\\
Answer b: 0.96\\
Answer c: 0.98\\
Answer d: We cannot answer because data is missing.