Question

1. oh henry candy bars have a mean mass of 250 g with a standard deviation of 5 grams. assuming a normal distribution, answer the following questions.

a) what percentage of oh henry bars will have a mass between 245 g and 255 g? (1 mark)
b) if 10 000 bars are produced daily, how many will have a mass greater than 265 g? (3 marks)

Explanation:

Step1: Calculate the z - score for \(x = 245\)

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\). Given \(\mu = 250\) and \(\sigma=5\), for \(x = 245\), \(z_1=\frac{245 - 250}{5}=- 1\)

Step2: Calculate the z - score for \(x = 255\)

Using the same formula \(z=\frac{x-\mu}{\sigma}\), for \(x = 255\), \(z_2=\frac{255 - 250}{5}=1\)

Step3: Find the probability \(P(245<X<255)\)

We know that for a normal distribution \(P(-1<Z<1)\). Using the standard normal distribution table, \(P(Z < 1)=0.8413\) and \(P(Z<-1)=0.1587\). Then \(P(-1 < Z < 1)=P(Z < 1)-P(Z<-1)=0.8413-0.1587 = 0.6826\)

Answer:

\(68.26\%\)