The weights of the chocolate in Hershey Kisses are normally distributed with a mean of 4.5338 g and a standard deviation of 0.1039 g.

For the bell-shaped graph of the normal distribution of weights of Hershey Kisses, what Is the area under the curve?

What is the value of the median?

What is the value of the mode?

What is the value of the variance?

For the bell-shaped graph of the normal distribution of weights of Hershey Kisses, what is the area under the curve?
(Type an integer or a decimal. Do not round.)

What is the value of the median?
g (Round to four decimal places as needed.)

What is the value of the mode?
g (Round to four decimal places as needed.)

What is the value of the variance?
9? (Round to four decimal places as needed.)

Assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of = 1.4 kg and a stand:

= 5.2 kg. Complete parts (a) through (c) below.

a. If 1 male college student is randomly selected, find the probability that he gains between 0 kg and 3 kg during freshman year.

The probability is ____

(Round to four decimal places as needed.)

b. If 4 male college students are randomly selected, find the probability that their mean weight gain during freshman year is between 0 kg and 3 kg.

The probability is ____

(Round to four decimal places as needed.)

c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?

◯ A. Since the weight gain exceeds 30, the distribution of sample means is a normal distribution for any sample size.

◯ B. Since the distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size.

◯ C. Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any 

◯ D. Since the distribution is of sample means, not individuals, the distribution is a normal distribution for any sample size.

Assume that a randomly selected subject is given a bone density test. Bone density test scores are normally distributed with a mean of 0 and a standard deviation of 1. Draw a graph and find , the 9th percentile. This is the bone density score separating the bottom 9% from the top 91%.

Which graph represents ? Choose the correct graph below.

(Please see the attachment)

The bone density score corresponding to is ____.

(Round to two decimal places as needed.)

A study was done using a treatment group and a placebo group. The results are shown in the table. Assume that the taro samples are Independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.01 significance level for both parts.

a. Test the claim that the two samples are from populations with the same mean

What are the null and alternative hypotheses?

A.  

     

B.  

      

 

C.  

      

 

D.  

      

The test statistic, t, is ____. (Round to two decimal places as needed.)

The P-value is ____

(Round to three decimal places as needed.)