Answer:
111
Explanation:
The sample mean is within 1.3units of the population mean, therefore the margin of error (E) = 1.3
confidence (C) = 90% = 0.9
α = 1 - C = 1 - 0.9 = 0.1
α/2 = 0.1 / 2 = 0.05
The z value for a confidence of 90% = z value of α/2 = z value of 0.45 (0.5 - 0.05) = 1.645
Given that E = 1.3, standard deviation (σ) and sample size = n.
The margin of error (E) is given by:
[tex]E=Z_\frac{\alpha}{2}*\frac{\sigma}{\sqrt{n} } \\\\Substituting:\\\\1.3=1.645*\frac{8.3}{\sqrt{n} }\\\\\sqrt{n}= 1.645*\frac{8.3}{1.3}\\\\\sqrt{n} =10.5\\\\n=110.3[/tex]
n ≈ 111 (to the next whole number)
