Answer:
I 90%(μ)= [69.648;71.951]
Step-by-step explanation:
The confidence interval formula is:
I (1-alpha) (μ)= mean+- [(Z(alpha/2))* σ/sqr(n)]
alpha= is the proposition of the distribution tails that are outside the confidence interval. In this case, 10% because 100-90%
Z(5%)= is the critical value of the standardized normal distribution. In this case is 1.645
σ= standard deviation. In this case 2.8 inches
mean= 70.8 inches
n= number of observations
Then, the confidence interval (90%):
I 90%(μ)= 70.8+- [1.645*(2.8/sqr(16))
I 90%(μ)= 70.8+- [1.1515)
I 90%(μ)= [70.8-1.1515;70.8+1.1515]
I 90%(μ)= [69.6485;71.9515]
I 90%(μ)= [69.648;71.951]
