Answer:
Step-by-step explanation:
To find the Taylor series of sinc(x) we will use the taylor series of sin(x). We have that
which is the taylor series expansion based at 0. Then for , by dividing both sidex by x, we have that
which is the taylor series expansion for the sinc function. Since the series of sine converges for every value of x. Then the taylor series of sinc converges for every value of x, but 0.
Answer:
At the 5% level, BAOI can infer that the average time to complete does not exceeds 60 hours.
Step-by-step explanation:
From the question we are told that
The population mean is
The sample size is
The sample mean is
The standard deviation is
The null hypothesis is
The alternative
Here we would assume the level of significance of this test to be
Next we will obtain the critical value of the level of significance from the normal distribution table, the value is
Generally the test statistics is mathematically represented as
substituting values
Looking at the value of t and we see that
hence we fail to reject the null hypothesis
This means that there no sufficient evidence to conclude that it takes more than 60 hours to complete the course
So
At the 5% level, BAOI can infer that the average time to complete does not exceeds 60 hours.
Answer:
35.2% probability that the sample mean will be 246 pages or more
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central 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 question, we have that:
What the probability that the sample mean will be 246 pages or more?
This is 1 subtracted by the pvalue of Z when X = 246. So
By the Central Limit Theorem
has a pvalue of 0.6480.
1 - 0.6480 = 0.3520
35.2% probability that the sample mean will be 246 pages or more