Question

How hot is the air in the top (crown) of a hot air balloon? Information from Ballooning: The Complete Guide to Riding the Winds, by Wirth and Young (Random House), claims that the air in the crown should be an average of 100°C for a balloon to be in a state of equilibrium. However, the temperature does not need to be exactly 100°C. What is a reasonable and safe range of temperatures? This range may vary with the size and (decorative) shape of the balloon. All balloons have a temperature gauge in the crown. Suppose that 55 readings (for a balloon in equilibrium) gave a mean temperature of x = 97°C. For this balloon, σ ≈ 19°C.

Compute a 95% confidence interval for the average temperature at which this balloon will be in a steady-state equilibrium. (Round your answers to one decimal place.)

Lower Limit =

Upper Limit =

Answer 1

Solution :

Given that,

Z/2 = Z_0.05 = 1.96

Margin of error = E = Z/2 * ( /n)

= 1.96 * ( 19 /  55 )

= 5.02

At 95% confidence interval estimate of the population mean is,

- E < < + E

97 - 5.0 <   < 97 + 5.0

92.0 <   < 102.0

lower limit = 92.0

upper limit = 102.0