Answer:
4.28 grams
Explanation:
The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by the formula:
[tex]z=\frac{x-\mu}{\sigma} \\\\where\ \mu=mean,\sigma=standard \ deviation,\ x=raw\ score[/tex]
Given that:
P(x > 5.1 grams) = 5%, x = 5.1 grams, σ = 0.5 grams
P(x > 5.1 grams) = 5%
P(x < 5.1 grams) = 100% - 5% = 95%
P(x < 5.1) = 95%
From the normal distribution table, 95% corresponds with a z score of 1.645. Hence:
[tex]1.64=\frac{5.1-\mu}{0.5}\\\\5.1-\mu=0.82\\\\\mu=4.28\ grams[/tex]
