Answer:
The interval is (2.7512, 2.8488)
Step-by-step explanation:
Given that:
The mean (μ) = 2.9 hours
The standard deviation (σ) = 0.24 hours
n = 14 pound turkey
The confidence interval (c) = 95% = 0.95
α = 1 - 0.95 = 0.05
[tex]\frac{\alpha }{2} = \frac{0.05}{2} = 0.025[/tex]
The Z score of [tex]\frac{\alpha }{2}[/tex] is the z score of 0.025 which is the same z score of 0.475 (0.5 - 0.025).
[tex]Z_{\frac{\alpha }{2} }=1.96[/tex]
[tex]\mu_x=\mu=2.9[/tex]
[tex]\sigma_x=\frac{\sigma}{\sqrt{n} }=\frac{0.24}{\sqrt{10} } =0.07589[/tex]
Therefore the margin of error E is given as
E = [tex]Z_{\frac{\alpha }{2} } *\sigma_x[/tex] = 1.96 × 0.0759 = 0.1488
The interval is [tex](\mu_x-E,\mu_x+E)[/tex] = (2.9 - 0.1488, 2.9 + 0.1488) = (2.7512, 2.8488)
The interval is (2.7512, 2.8488)
