Question

The weights of bags of baby carrots are normally distributed, with a mean of 32 ounces and a standard deviation of 0.36 ounce.

A) Sketch the distribution of weights and label the mean, µ, and label two standard deviations in both directions on the sketch.

B) Bags that weigh more than 32.6 oz are considered too heavy and must be repackaged. What percentage of bags of baby carrots will need to be repackaged? (1) Draw a new picture and shade the area in question. (2) Show your work and provide your final answer as a sentence in the context of the problem.

C) In what interval should the factory expect to find the middle 50% of weights for the bags of baby carrots? Use this information to calculate the IQR for this data. (1) Draw a new picture and shade the area in question. (2) Show your work and provide your final answer as a sentence in the context of the problem.

Answer 1

C)

IQR is the range of scores which contain 50% of the data between it

Z = 0.6745 and Z = - 0.6745 contain 50% of all the values

Z = (X - $\mu$ )/ $\sigma$

X1 = Z $\sigma$ +  $\mu$

= 32 + 0.6745*0.36

= 32.24

X2 = 32 - 0.6745*0.36

= 31.76

50% of weights of bags would lie between 32.24 and 31.76 Ounces.