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avanturin [10]
2 years ago
11

IQ scores are normally distributed with a mean of 100 and a standard deviation of 16.

Mathematics
1 answer:
Alenkasestr [34]2 years ago
8 0

Answer:

<u>Given</u>

  • μ = 100
  • σ = 16

a)

x = 68

  • z = (x - μ)/σ =
  • (68 - 100)/16 = -2
  • z-score = 0.0228 = 2.28%

b)

x = 100 and x = 132

  • z = (100 - 100)/16 = 0, z-score = 50%
  • z = (132 - 100)/16 = 2, z-score = 0.9772 = 97.72%
  • 97.72% - 50% = 47.72%

c)

68% confidence interval, <u><em>assumed sample number n = 100</em></u>

z-score representing 68% = 0.47

  • CI = μ ± z× σ/√n
  • CI = 100 ± 0.47*16/√100 =
  •     = 100 ± 0.752

d)

  • n = 10000
  • x = 148
  • z = (148 - 100)/16 = 3, z-score is 0.9987  

<u>Number of people scored above 148:</u>

  • (1 - 0.9987)*10000 = 13 people
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