Answer:
55 adult tickets were sold on Friday.
Step-by-step explanation:
A linear system will be used to model the system.
Let c be the number of child tickets and a be the number of adult tickets
Then according to given statements
From equation 1
Putting this in equation 2
Putting c = 78 in equation 1
Hence,
55 adult tickets were sold on Friday.
Answer: 95% confidence interval = 20,000 ± 2.12
( 19228.736 , 20771.263 ) OR ( 19229 , 20771 )
Step-by-step explanation:
Given :
Sample size(n) = 17
Sample mean = 20000
Sample standard deviation = 1,500
5% confidence
∴ = 0.025
Degree of freedom () = n-1 = 16
∵ Critical value at ( 0.025 , 16 ) = 2.12
∴ 95% confidence interval = mean ±
Critical value at 95% confidence interval = 20,000 ± 2.12
( 19228.736 , 20771.263 ) OR ( 19229 , 20771 )
Answer:
(a) The probability that the thickness is less than 3.0 mm is 0.119.
(b) The probability that the thickness is more than 7.0 mm is 0.119.
(c) The probability that the thickness is between 3.0 mm and 7.0 mm is 0.762.
Step-by-step explanation:
We are given that thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally distributed, with a mean of 5.0 millimeters (mm) and a standard deviation of 1.7 mm.
Let X = <u><em>thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village.</em></u>
So, X ~ Normal()
The z-score probability distribution for the normal distribution is given by;
Z = ~ N(0,1)
where, = population mean thickness = 5.0 mm
= standard deviation = 1.7 mm
(a) The probability that the thickness is less than 3.0 mm is given by = P(X < 3.0 mm)
P(X < 3.0 mm) = P( <
) = P(Z < -1.18) = 1 - P(Z
1.18)
= 1 - 0.8810 = <u>0.119</u>
The above probability is calculated by looking at the value of x = 1.18 in the z table which has an area of 0.881.
(b) The probability that the thickness is more than 7.0 mm is given by = P(X > 7.0 mm)
P(X > 7.0 mm) = P( >
) = P(Z > 1.18) = 1 - P(Z
1.18)
= 1 - 0.8810 = <u>0.119</u>
The above probability is calculated by looking at the value of x = 1.18 in the z table which has an area of 0.881.
(c) The probability that the thickness is between 3.0 mm and 7.0 mm is given by = P(3.0 mm < X < 7.0 mm) = P(X < 7.0 mm) - P(X 3.0 mm)
P(X < 7.0 mm) = P( <
) = P(Z < 1.18) = 0.881
P(X 3.0 mm) = P(
) = P(Z
-1.18) = 1 - P(Z < 1.18)
= 1 - 0.8810 = 0.119
The above probability is calculated by looking at the value of x = 1.18 in the z table which has an area of 0.881.
Therefore, P(3.0 mm < X < 7.0 mm) = 0.881 - 0.119 = 0.762.