The student's statement about area is incorrect because by joining suitable lines, we can divide the region into 3 rectangles and we can find its area.
Please check the attached figure.
From the figure, we can easily observe that the area of the shaded region = Area of the rectangle A + Area of the rectangle B - Area of the rectangle C.
Answer:
a) P(12.99 ≤ X ≤ 13.01) = 0.3840
b) P(X ≥ 13.01) = 0.3075
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the cental limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
(a) Calculate P(12.99 ≤ X ≤ 13.01) when n = 16.
Here we have
This probability is the pvalue of Z when X = 13.01 subtracted by the pvalue of Z when X = 12.99.
X = 13.01
By the Central Limit Theorem
has a pvalue of 0.6915
X = 12.99
has a pvalue of 0.3075
0.6915 - 0.3075 = 0.3840
P(12.99 ≤ X ≤ 13.01) = 0.3840
(b) How likely is it that the sample mean diameter exceeds 13.01 when n = 25?
P(X ≥ 13.01) =
This is 1 subtracted by the pvalue of Z when X = 13.01. So
has a pvalue of 0.6915
1 - 0.6915 = 0.3075
P(X ≥ 13.01) = 0.3075
Answer:
The price of a sandwich is £2.5 and the price of a croissant is £2
Step-by-step explanation:
Let s be the number of sandwiches and c be the number of croissants
Then according to given statements the equations will be:
Multiplying equation 1 by 2 and subtracting equation 2 from the new equation
Now
Putting s=2.5 in equation 1
Hence,
The price of a sandwich is £2.5 and the price of a croissant is £2
Answer:
To pack 1872 muffins the mini muffins company needs 156 large boxes.
Step-by-step explanation:
Number of muffins baked by the mini muffins company = 1872.
the large mini muffin boxes hold a dozen muffins that is the large box contains 12 muffins.( 1 Dozen = 12 )
We have to find the number of large boxes needed to pack 1872 muffins.
Using unitary method,
12 muffins is contained in 1 large box.
1 muffin is contained in large box.
1872 muffins contained in large boxes.
Hence, To pack 1872 muffins the mini muffins company needs 156 large boxes.