Statistics assigment | Mathematics homework help

1. Heights of men on a basketball team have a bell shaped distribution with a mean of 182cm and a standard deviation of 8cm. Using the empirical rule, what is the approximate percentage of the men between the following values?

a.166cm and 198cm

b.158 cm and 206cm


a.___ % of the men are between 166 cm and 198 cm

b.___% of  the men are between 158 cm and 206 cm.


2. Below are 36 sorted ages of an acting award winner. Find P75 using the method presented in the textbook.


18     19    23    31    33    33    36    37    39    42

49     49    50    55    55    59    61    62    63    64

64     65    65    69    70    70    71    72    72    74 

75    75    76     77    78    79




3. In the accompanying table, the random variable x represents the number of television in a household in a certain country. Determine whether or not the table is a probability distribution. If it is probability distribution, find its mean and standard deviation. (SHOW WORK)

x       P(x)

0      0.04

1      0.11

2      0.28

3      0.33

4      0.13

5      0.11


Is the table a probability distribution? yes or no


If the table is a probability distribution, what is its mean?


Is the table is a probability distribution, what is its standard deviation?


4. Assume the readings on a thermometer are normally distributed with a mean of 0degreesC and a standard deviation of 1.00 degrees C. Find the probability that a randomly selected thermometer reads between -2.12 and -0.68.


5. A survey found that women’s heights are normally distributed with a mean 63.8in and standard deviation 2.3 in. A branch of the military requires women’s heights to be between 58 in and 80 in. (SHOW WORK)

a. Find the percentage of women meeting the height requirement. Are many women being denied the opportunity to join this branch of the military because they are too short or tall?

b. If this branch of the military changes the height requirements so that all women are eligible except the shortest 1% and the tallest 2% what the new height requirements?


a. The percentage of women who meet the height requirement ___%

 Are many women being denied the opportunity to join this branch of the military because they are too short or too tall? Yes or No


b. For the new height requirements, this branch of military requires women height to be at least ____in and at most ____ in.


6. If np > 5 and nq > 5 estimate P9 more thank 6) with n=11 and p= 0.4 by using the normal distribution as an approximation to the binomial distribution, if np < 5 or nq < 5  then state that the normal approximation is not suitable.

a. P(more than 6)= ___ or

b  The normal distribution cannot be used


7. In a test of the effectiveness of garlic for lowering cholesterol, 49 subjects were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes in their LDL cholesterol have a mean of 3.1 and a standard deviation of 1.5. Complete parts below.


a. What is the best point estimate of the population mean net change in LDL cholesterol after the garlic treatment?  The best point estimate is ____ mg/dL.

b. Construct a 95% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL cholesterol?

What is the confidence interval estimate of the population mean U?

_____ mg/dL < u < ____mg/dL.


8. Assume that the significance level is a = 0.01. Use the given information to find the P value and the critical value(s)

With H1:p+1/3 the test statistic is z= -1.56

P value =____

The critical value is/ are ___


9. In a study of pregnant women and their ability to correctly predict the sex of their baby, 59 of the pregnant women had 12 years of education or less than 39% of them correctly predicted the sex of their baby. Use a 0.05 significance level to test the claim that these women have no ability to predict the sex of their baby and the results are not significantly different from those that would be expected with random guesses. Identify the null hypothesis, test statistic, P-value, conclusion about null hypothesis, and final conclusion that addresses the original claim.


The test statistic is z=____


The P-value____


10. Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative hypotheses, te4st statistic, P-value, critical value(s) and state the final conclusion that addresses the original claim.


A simple random sample of 25 filtered 100mm cigarettes is obtained and the tar content of each cigarette is measured. The sample has a mean of 19.0 mg and a standard deviation of 3.13 mg. Use a 0.05 significance level to test the claim that the mean tar content of filtered 100 mm cigarettes is les than 21.1 mg. which is the mean for unfiltered king size cigarettes. What do the results suggest, if anything about the effectiveness of the filters?


Identify the test statistics



Identify the P-value



The critical value____


11.  The blood pressure measurements of a single patient were taken by twelve different medical students an the results are listed below. Find the value of the linear correlation coefficient and the the P-value using a=0.05. Is there sufficient evidence to conclude that there is a linear correlation between systolic measurements and diastolic measurements?


Systolic(x)   135      130     139     119     125     120     129     132     135     145     142     137

Diastolic(y)    91        94        99      81        88       83       83        83        81       96     104      90


The linear correlation coefficient r ___


The test statistic  t is ____


The P- value is _____


12.  Suppose IQ scores were obtained from randomly selected siblings. For 20 such pairs of people, the linear correlation coefficient is 0.842 and the equation of the regression line is y= 6.12 + 0.92x, where x represents the IQ score o the older child. Also the 20 x values have a mean of 98.59 and the 20 y values have a mean of 97.05. What I the predicted IQ of the younger child given that the older child has an IQ of 106? Use a significance level of 0.05.


The best predicted IQ of the younger child is_____

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