Answer:
a) 
b) From the central limit theorem we know that the distribution for the sample mean 
is given by:
c) 
Step-by-step explanation:
Let X the random variable the represent the scores for the test analyzed. We know that:
And we select a sample size of 64.
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
Part a
For this case the mean and standard error for the sample mean would be given by:
Part b
From the central limit theorem we know that the distribution for the sample mean is given by:
Part c
For this case we want this probability:
And we can use the z score defined as:
And using this we got:
And using a calculator, excel or the normal standard table we have that:
Answer:
Sample: few thousand adults
Population: all the adults
Step-by-step explanation:
A sample is a subset of the population, selected randomly.
In this case:
The sample consist of the few thousand adults selected to determine the opinions about the National polls.
The population consist of all the adults belonging to the said nation.
Consider an example about the new President election.
To determine which of the two candidates (say <em>A</em> and <em>B</em>) has a higher probability of winning the President election, the election society took a random sample of voters and asked who they think will be a better president.
The sample selected will be large enough, probably 10% of the population of all voters.
From this study it can be estimated which candidate has the higher chance of winning.
The probability of rolling an odd number or a number less than 5 is 5/6.
Probability is the likelihood of the occurrence of an event. It is the ratio of number of events to number of possible outcomes.
The possible outcome from rolling a six-sided die is 1, 2, 3, 4, 5 and 6
P(odd number) = 3/6; P(less than 5) = 4/6; P(odd number and less than 5) = 2/6
Hence:
P(odd number or less than 5) = 3/6 + 4/6 - 2/6 = 5/6
The probability of rolling an odd number or a number less than 5 is 5/6.
Answer:
Option (2). 14 m
Step-by-step explanation:
Formula to get the area of a circle 'A' = 
where r = radius of the circle
Given in the question,
Area of the circle = 153.86 square meters
By putting the values in the formula,
153.86 = πr²
r = 
r = 
r = 7 meters
Diameter of circle = 2 × (radius of the circle)
= 2 × 7
= 14 meters
Therefore, diameter of the circle is 14 meters.
Option (2) is the answer.
