In Exercises 29 and 30, use the Empirical Rule. /m 29, The mean rate for satelli
ID: 3196140 • Letter: I
Question
In Exercises 29 and 30, use the Empirical Rule. /m 29, The mean rate for satellite television for a sample of households was $70.00 per month, with a standard deviation of $14.50 per month. Between what two values do 99.7% of the data lie? (Assume the data set has a bell-shaped distribution.) 30. The mean rate for satellite television for a sample of households was $72.50 per month, with a standard deviation of $12.50 per month. Estimate the percent of satellite television rates between $60.00 and $85.00. (Assume the data set has a bell-shaped distribution.)Explanation / Answer
Ans 29
Now, we need to find the range for 99.7% of the data.
We know that, P(-3<Z<3) = 99.7%
Let the rate variable = X
=> Z = ( X - 70)/14.50
=> -3 < ( X - 70)/14.50 < 3
=> 26.5 < X < 113.5
So, 99.7% of the data will lie between $26.50 and $113.50
Ans 30.
Let the rate variable = X and 60 < X < 85
=> Z = ( X - 72.5 )/12.5
=> ( 60 - 72.5 ) / 12.5 < Z < ( 85 - 72.5 ) / 12.5
=> -1 < Z < 1
=> P ( 60 < X < 85 ) = P ( -1 < Z < 1 ) = 68.27%