In a small factory producing bamboo products, the standard acceptable measurement for a bamboo straws’ lengths are between 10.085 cm and 12.075 cm. Alexis has noticed that 6% of the straws are rejected for being too short and another 6% are rejected for being too tall. What is the mean and standard deviation of distribution assuming that the straws’ lengths are normally distributed? (2dp)
Answers
Mean = 11.08 cm & SD = 0.64 cm
Step-by-step explanation:
lengths are between 10.085 cm and 12.075 cm
SD = Standard Deviation
6% of the straws are rejected for being too short
=> 6 % are below 10.085 cm
z = -1.555
=> -1.555 = (10.085 - Mean)/SD
=> 1.555SD = Mean - 10.085
and another 6% are rejected for being too tall
=> 100 - 6 = 94 % are less than 12.075 cm
=> z = 1.555
=> 1.555 = (12.075 - Mean)/SD
=> 1.555SD = 12.075 - Mean
Equating both
Mean - 10.085 = 12.075 - Mean
=> 2 Mean = 22.16
=> Mean = 11.08
1.555SD = Mean - 10.085
=> 1.555SD = 11.08 - 10.085
=> 1.555SD = 0.995
=> SD = 0.64
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