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 ≈ 14°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,

Z/2 = 1.96

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

= 1.96 * (14 / 55)

= 3.7

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

- E < < + E

97 - 3.7 < < 97 + 3.7

93.3 < < 100.7

(93.3 , 100.7)

Lower limit = 93.3 o C

Upper limit = 100.7 o C

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