Answer: 72.78% of the drivers are traveling between 70 and 80 miles per hour based on this distribution.
Step-by-step explanation:
Let X be a random variable that represents the speed of the drivers.
Given: population mean : M = 72 miles ,
Standard deviation: s= 3.2 miles
The probability that the drivers are traveling between 70 and 80 miles per hour based on this distribution:
![P(70\leq X\leq 80)=P(\frac{70-72}{3.2}\leq \frac{X-M}{s}\leq\frac{80-72}{3.2})\\\\= P(-0.625\leq Z\leq 2.5)\ \ \ \ \ [Z=\frac{X-M}{s}]\\\\=P(Z\leq2.5)-P(Z\leq -0.625)\\\\\\ =0.9938-0.2660\ \ \ [\text{Using p-value calculator}]\\\\=0.7278](https://tex.z-dn.net/?f=P%2870%5Cleq%20X%5Cleq%2080%29%3DP%28%5Cfrac%7B70-72%7D%7B3.2%7D%5Cleq%20%5Cfrac%7BX-M%7D%7Bs%7D%5Cleq%5Cfrac%7B80-72%7D%7B3.2%7D%29%5C%5C%5C%5C%3D%20P%28-0.625%5Cleq%20Z%5Cleq%202.5%29%5C%20%5C%20%5C%20%5C%20%5C%20%5BZ%3D%5Cfrac%7BX-M%7D%7Bs%7D%5D%5C%5C%5C%5C%3DP%28Z%5Cleq2.5%29-P%28Z%5Cleq%20-0.625%29%5C%5C%5C%5C%5C%5C%20%3D0.9938-0.2660%5C%20%5C%20%5C%20%5B%5Ctext%7BUsing%20p-value%20calculator%7D%5D%5C%5C%5C%5C%3D0.7278)
Hence, 72.78% of the drivers are traveling between 70 and 80 miles per hour based on this distribution.
Answer: convert 15% to a decimal. 0.15 times 75 is 11.25
Converting Percentages to Decimals
Easiest—divide by 100: The simplest way to convert a percentage to a decimal is to divide the number (in percentage format) by 100.
Move the decimal: Another way to convert a quoted percentage to decimal format is to move the decimal two places to the left
Answer:
36 boards
Step-by-step explanation:
The boards are as long as the room, so I only had to worry about the width. If the boards were 1/2 ft wide, I would need 2 boards for every foot of width. For 16 ft, I would need 32 boards.
Instead of dividing, I wrote the equivalent multiplication by multiplying by the reciprocal of 11/24 (the reciprocal of 11/24 is 24/11)
I simplified by dividing both 2 and 24 by 2, and both 11 and 33 by 11.
Therefore he needs 36 boards
As is the case for any polynomial, the domain of this one is (-infinity, +infinity).
To find the range, we need to determine the minimum value that f(x) can have. The coefficients here are a=2, b=6 and c = 2,
The x-coordinate of the vertex is x = -b/(2a), which here is x = -6/4 = -3/2.
Evaluate the function at x = 3/2 to find the y-coordinate of the vertex, which is also the smallest value the function can take on. That happens to be y = -5/2, so the range is [-5/2, infinity).
1 and 1/4..................................
