Answer:
0.6710
Step-by-step explanation:
The diameters of ball bearings are distributed normally. The mean diameter is 107 millimeters and the population standard deviation is 5 millimeters.
Find the probability that the diameter of a selected bearing is between 104 and 115 millimeters. Round your answer to four decimal places.
We solve using z score formula
z = (x-μ)/σ, where
x is the raw score
μ is the population mean = 107 mm
σ is the population standard deviation = 5 mm
For x = 104 mm
z = 104 - 107/5
z = -0.6
Probability value from Z-Table:
P(x = 104) = 0.27425
For x = 115 mm
z = 115 - 107/5
z = 1.6
Probability value from Z-Table:
P(x = 115) = 0.9452
The probability that the diameter of a selected bearing is between 104 and 115 millimeters is calculated as:
P(x = 115) - P(x = 104)
0.9452 - 0.27425
= 0.67095
Approximately = 0.6710
Answer:
![\left[\begin{array}{ccc}5&7\\5&-8\\3&-9\end{array}\right] \left[\begin{array}{ccc}c\\d\end{array}\right] =\left[\begin{array}{ccc}-16\\3\\-15\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%267%5C%5C5%26-8%5C%5C3%26-9%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dc%5C%5Cd%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-16%5C%5C3%5C%5C-15%5Cend%7Barray%7D%5Cright%5D)
This tells us that:
![A=\left[\begin{array}{ccc}5&7\\5&-8\\3&-9\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%267%5C%5C5%26-8%5C%5C3%26-9%5Cend%7Barray%7D%5Cright%5D)
![b=\left[\begin{array}{ccc}-16\\3\\-15\end{array}\right]](https://tex.z-dn.net/?f=b%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-16%5C%5C3%5C%5C-15%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
So we are saying we have scalars, c and d, such that:
![c\left[\begin{array}{ccc}5\\5\\ 3\end{array}\right]+d\left[\begin{array}{ccc}7\\-8\\-9\end{array}\right]=\left[\begin{array}{ccc}-16\\3\\-15\end{array}\right]](https://tex.z-dn.net/?f=c%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%5C%5C5%5C%5C%203%5Cend%7Barray%7D%5Cright%5D%2Bd%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D7%5C%5C-8%5C%5C-9%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-16%5C%5C3%5C%5C-15%5Cend%7Barray%7D%5Cright%5D)
.
So we want to find a way to express this as:
Ax=b where x is the scalar vector, ![\left[\begin{array}{ccc}c\\d\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dc%5C%5Cd%5Cend%7Barray%7D%5Cright%5D)
.
So we can write this as:
Answer:
There’s no answer
Step-by-step explanation:
