Answer:
55
Explanation:
The z score is a score used in statistics to determine how many standard deviations the raw score is above or below the mean.it is given by the formula:
[tex]z=\frac{x-\mu}{\sigma}\\ Where\ \mu \ is\ the\ mean, x\ is\ the\ raw\ score\ and\ \sigma\ is\ the\ standard\ deviation[/tex]
Given that:
σ = 8, P(z > 58) = 0.3413, x > 58/ Hence:
P(z < 58) = 1 - P(z > 58) = 1 - 0.3413 = 0.6587
P(z < 58) = 0.6587
From the normal distribution table, P(z < 58) = 0.6587 corresponds with a z score of 0.41
[tex]z=\frac{x-\mu}{\sigma}\\ \\0.41=\frac{58-\mu}{8}\\\\Cross-multiplying:\\\\58-\mu=3.28\\\\\mu=58-3,28\\\\\mu=54.72[/tex]
μ ≅ 55
