Question

# How hot is the air in the top (crown) of a hot air balloon? Information from...

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 ≈ 21°C.

(a) 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 °C upper limit °C

95% confidence interval for is

- Z * / sqrt(n ) < < + Z * / sqrt(n )

97 - 1.96 * 21 / sqrt(55) < < 97 + 1.96 * 21 / sqrt(55)

91.4 < < 102.6

Lower limit = 91.4 oC

Upper limit = 102.6 oC

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