A manufacturer produces piston rings for an automobile engine. It is known that ring diameter is normally distributed with σ=0.0
1 answer:
<h2>Answer with explanation:</h2>
The confidence interval for population mean is given by :-
(1)
, where = sample mean
z* = critical value.
SE = standard error
and ,
= population standard deviation.
n= sample size.
As per given , we have
n= 15
It is known that ring diameter is normally distributed.
By z-table ,
The critical value for 95% confidence = z*= 1.96
A 99% two-sided confidence interval on the true mean piston diameter :
(using (1))
[Rounded to three decimal places]
∴ A 99% two-sided confidence interval on the true mean piston diameter = (74.020, 74.022)
By z-table ,
The critical value for 95% confidence = z*= 1.96
A 95% lower confidence bound on the true mean piston diameter:
(using (1))
[Rounded to three decimal places]
∴ A 95% lower confidence bound on the true mean piston diameter= 74.020
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Answer:
a) Find the probability that the drink is less than 11.9 fluid ounces
We are supposed to find P(x<11.9)
x= 11.9
We will use z score formula :
Refer the z table
So, P(z<-0.67) = 0.2514
Hence the probability that the drink is less than 11.9 fluid ounces is 0.2514
b)Find the probability that the drink is between 11.6 and 11.9 fluid ounces
x= 11.6
We will use z score formula :
x= 11.9
We will use z score formula :
We are supposed to find P(11.6<x<11.9)
So, P(11.6<x<11.9)= P(x<11.9)-P(x<11.6)
P(-1.67<z<-0.67)= P(z<-0.67)-P(z<-1.67)
Refer the z table
P(-1.67<z<-0.67)= P(z<-0.67)-P(z<-1.67)
P(-1.67<z<-0.67)= 0.2514-0.0475
P(-1.67<z<-0.67)= 0.2039
So, the probability that the drink is between 11.6 and 11.9 fluid ounces is 0.2039.
c)Find the probability that the drink is more than 12.6 fluid ounces
We are supposed to find P(x>12.6)
x= 12.6
We will use z score formula :
Refer the z table
P(x>12.6)=1-P(x<12.6)
P(z>1.67)=1-P(z<1.67)
P(z>1.67)=1-0.9525
P(z>1.67)=0.0475
Hence the probability that the drink is more than 12.6 fluid ounces is 0.0475
d) Is the drink containing more than 12.6 fluid ounces an unusual event?
Since p value is less than alpha (0.05)
Answer = No, because the probability that a drink containing more than 12.6 fluid ounces is less than 0.05, this event is not unusual.
Answer:
Step-by-step explanation:
1.
sum > 8 or 9,10,11,12
events sum >8 are 36,45,54,63,46,55,64,56,65,66
no. of events=10
p=10/36=5/18
2.
P=291/2237
3.
4.
a.
P=5/246
b.
p=208/246=104/123
5.
yes no total
student 56 42 98
teacher 3 7 10
total 59 49 108