Answer:
The probability is 
Step-by-step explanation:
From the question we are told that
The sample size is n = 175
The population proportion is p = 0.45
Generally the mean of the sampling distribution is 
Generally the standard deviation is mathematically represented as

=> 
=> 
Generally the probability of that the sample proportion of orange candies will be between 0.35 and 0.55 is

=> 
Generally 
So

=> 
From the z-table

and

So

=> 
Answer:
a) 0.1984
b) No. Is not too small to support the conjecture with confidence
Step-by-step explanation:
1) Previous concepts and data given
The sample sizes are 
We can find the distribution for
, and since is a sampling distribution and
and
follows normal distributions then
follows a normal distribution too.
The mean and the deviation for
is given by:
and since
then 

Since both A and B have the same deviation and variance then:

2) Part a
We want to find:

The random variable
follows a normal distribution with mean 0 and deviation 1 we can use this:


3) Part b
From part a we found that we have a change of 19.84% that the experiment would give a difference between the sample means which is greater or equal than 0.2
Analyzing the probability obtained we can say that is not too small to support the conjecture with confidence that the population means for the two machines are different