Question

the weights of bags of baby carrots are normally distributed, with a mean of 34 ounces and a standard deviation of .35 ounces. bags in the upper 4.5% are too ehavy and must be repackaged. what is the most a bag of baby carrots can weigh and does not need to be repackaged

Answer 1

Answer:

The carrots can weight atmost 34.59 ounces so that it does not need to be repackaged.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 34 ounces

Standard Deviation, σ = 0.35 ounces

We are given that the distribution of weights of bags is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

We have to find the value of x such that the probability is 0.045

$P( X > x) = P( z > \displaystyle\frac{x - 34}{0.35})=0.045$  

$= 1 -P( z < \displaystyle\frac{x - 34}{0.35})=0.045$  

$=P( z < \displaystyle\frac{x - 34}{0.35})=0.955$  

Calculation the value from standard normal z table, we have,  

$\displaystyle\frac{x - 34}{0.35} = 1.695\\\\x = 34.59325\approx 34.59$  

Thus, the carrots can weight atmost 34.59 ounces so that it does not need to be repackaged.