1)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 53 readings (for a balloon in equilibrium) gave a mean temperature of x = 97°C. For this balloon, σ ≈ 13°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 °Cupper limit °C(b) If the average temperature in the crown of the balloon goes above the high end of your confidence interval, do you expect that the balloon will go up or down? Explain.It will go down because hot air will make the balloon fall.It will go down because hot air will make the balloon rise. It will go up because hot air will make the balloon rise.It will go up because hot air will make the balloon fall.2) We can use the random number table to simulate outcomes from a given discrete probability distribution. Jose plays basketball and has probability 0.7 of making a free-throw shot. Let x be the random variable that counts the number of successful shots out of 10 attempts. Consider the digits 0 through 9 of the random number table. Since Jose has a 70% chance of making a shot, assign the digits 0 through 6 to “making a basket from the free throw line” and the digits 7 through 9 to “missing the shot.”(a) Do 70% of the possible digits 0 through 9 represent “making a basket”?No. Seven of the 10 digits represent “making a basket.”Yes. Three of the 10 digits represent “making a basket.” Yes. Seven of the 10 digits represent “making a basket.”No. Three of the 10 digits represent “making a basket.”(b) Start at line 2, column 1 of the random number table. Going across the row, determine the results of 10 “trials.” How many free-throw shots are successful in this simulation? (c) Your friend decides to assign the digits 0 through 2 to “missing the shot” and the digits 3 through 9 to “making the basket.” Is this assignment valid? Explain.No. Three of the 10 digits represent “making a basket.”Yes. Seven of the 10 digits represent “making a basket.” Yes. Three of the 10 digits represent “making a basket.”No. Seven of the 10 digits represent “making a basket.”3) Using this information and the histograms shown above, construct a frequency table for the highway mileages of the same cars. Use class boundaries 16.5, 20.5, 24.5, 28.5, 32.5, 36.5, and 40.5.Class Boundaries Frequency − − − − − −
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