Answer:
The probability that the weight of a candy randomly selected is more than 0.8537 is 0.7486
Step-by-step explanation:
The given parameters are;
The mean candle weight = 0.8552 g
The standard deviation = 0.0519 g
The number in the sample, n = 442 candles
By central limit theorem, the sample standard deviation, [tex]\sigma _{\bar x}[/tex] is given by the relationship;
[tex]\sigma _{\bar x} = \dfrac{\sigma}{\sqrt{n} } = \dfrac{0.0519}{\sqrt{442} } = 0.002469[/tex]
The probability is given by the relation;
[tex]P\left (\bar{X}>0.8537 \right )= P\left (\dfrac{\bar{X}-\mu }{\dfrac{\sigma }{\sqrt{n}}} >\dfrac{0.8537-\mu }{\dfrac{\sigma }{\sqrt{n}}} \right )[/tex]
[tex]P\left (\bar{X}>0.8537 \right )= P\left (\dfrac{\bar{X}-0.8552 }{\dfrac{\sigma }{\sqrt{n}}} >\dfrac{0.8537-0.8552 }{\dfrac{0.0519 }{\sqrt{442}}} \right )[/tex]
[tex]P\left (\bar{X}>0.8537 \right )= P\left (z>-0.6076\right )[/tex]
The from the z-score table we have = 0.2514
The probability of P (z > -6076) = 1 - 0.2514 = 0.7486
The probability that the weight of a candy randomly selected is more than 0.8537 = 0.7486.
