Answer:
The two diameters that separate the top 5% and the bottom 5% are 5.51 and 5.65 respectively.
Step-by-step explanation:
We are given that the diameters of bolts produced in a machine shop are normally distributed with a mean of 5.58 millimeters and a standard deviation of 0.04 millimeters.
<em>Let X = diameters of bolts produced in a machine shop</em>
So, X ~ N()
The z score probability distribution is given by;
Z = ~ N(0,1)
where, = mean diameter = 5.58 millimeter
= standard deviation = 0.04 millimeter
<u>Now, we have to find the two diameters that separate the top 5% and the bottom 5%.</u>
- <u>Firstly, Probability that the diameter separate the top 5% is given by;</u>
P(X > x) = 0.05
P( > ) = 0.05
P(Z > ) = 0.05
<em>So, the critical value of x in z table which separate the top 5% is given as 1.6449, which means;</em>
= 1.6449
= 5.58 + 0.065796 = 5.65
<u />
- <u>Secondly, Probability that the diameter separate the bottom 5% is given by;</u>
P(X < x) = 0.05
P( < ) = 0.05
P(Z < ) = 0.05
<em>So, the critical value of x in z table which separate the bottom 5% is given as -1.6449, which means;</em>
= -1.6449
= 5.58 - 0.065796 = 5.51
Therefore, the two diameters that separate the top 5% and the bottom 5% are 5.51 and 5.65 respectively.
5 and 8/12= 5 and 2/3= 17/3
2 and 6/36= 2 and 1/6=13/6
17/3-13/6 Need common denominator
34/6-13/6=21/6=3.5 or 3 and 1/2
Answer:
After 20 months
Step-by-step explanation:
This is a compound growth problem which has the formula:
Where
F is future value
P is present amount
r is the rate of growth
t is the time (in months)
Future amount is $65, what he needs at-least
P is the initial amount, that is $10
r is the rate of growth, which is 10% or 10/100 = 0.1
t is time in months, what we need to find
Substituting and solving we get:
<u>He would need 19.64 months to save up at-least 65. So, that means, he would need 20 months</u>
Expressed as a fraction 56 is 56/35 of 35. That fraction can be reduced, and expressed several ways.
56/35 = 8/5 = 1 3/5 = 1.6
56 is 1 3/5 of 35
56 is 1.6 times 35
Answer:
66%
Step-by-step explanation: