A survey of 76 commercial airline flights of under 2 hours resulted in a sample average late time for a flight of 2.55 minutes. The population standard deviation was 12 minutes. Construct a 95% confidence interval for the average time that a commercial flight of under 2 hours is late. What is the point estimate? What does the interval tell about whether the average flight is late?

Since the time can't be negative a good approximation for the confidence interval would be (0,5.248) minutes. The interval are tellling to us that at 95% of confidence the average late time is lower than 5.248 minutes.

Step-by-step explanation:

Information given

[tex]\bar X=2.55[/tex] represent the sample mean for the late time for a flight

[tex]\mu[/tex] population mean

[tex]\sigma=12[/tex] represent the population deviation

n=76 represent the sample size

Confidence interval

The best point of estimate for the true mean is:

[tex]\hat \mu = \bar X = 2.55[/tex]

The confidence interval for the true mean is given by:

[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)

The Confidence level given is 0.95 or 95%, th significance would be [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. If we look in the normal distribution a quantile that accumulates 0.025 of the area on each tail we got [tex]z_{\alpha/2}=1.96[/tex]

Replacing we got:

[tex]2.55-1.96\frac{12}{\sqrt{76}}=-0.148[/tex]

[tex]2.55+1.96\frac{12}{\sqrt{76}}=5.248[/tex]

Since the time can't be negative a good approximation for the confidence interval would be (0,5.248) minutes. The interval are tellling to us that at 95% of confidence the average late time is lower than 5.248 minutes.