the times taken to assemble a clock at a factory are approximately normally distributed with a given mean…

the times taken to assemble a clock at a factory are approximately normally distributed with a given mean $mu = 3$ hr and standard deviation $sigma = 0.5$ hr. what percentage of the times are between 2 hr and 4 hr?\n34%\n47.5%\n68%\n95%

the times taken to assemble a clock at a factory are approximately normally distributed with a given mean $mu = 3$ hr and standard deviation $sigma = 0.5$ hr. what percentage of the times are between 2 hr and 4 hr?\n34%\n47.5%\n68%\n95%

Answer

Explanation:

Step1: Calculate z - scores

For (x = 2), (z_1=\frac{2 - 3}{0.5}=\frac{- 1}{0.5}=-2). For (x = 4), (z_2=\frac{4 - 3}{0.5}=\frac{1}{0.5}=2).

Step2: Use the empirical rule

The empirical rule for a normal distribution states that approximately 95% of the data lies within (z=-2) and (z = 2).

Answer:

95%