Question

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

v

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 56 readings (for a balloon in equilibrium) gave a mean temperature of x = 97°C. For this balloon, σ ≈ 22°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

Solution :

Given that,

Sample size = n = 56

Z /2 = 1.96

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

= 1.96 * (22 / 56)

= 5.8

At 95% confidence interval estimate of the population mean is, - E < < + E

97 - 5.8< < 97 + 5.8

91.2 < < 102.8

lower limit 91.20C

upper limit 102.80C

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