Statistics Week 2 | Complete Solution

Six different second year medical students at Bellevue hospital measured the blood pressure of the same person. The systolic readings (in mmHg) are listed below. Find the range, variance, and standard deviation for the given sample data. If the subjects blood pressure remains constant and the medical students correctly apply the same measurement technique, what should be the value of the standard deviation?

136, 129, 141, 139,138, 127

Range____________

Variance____________ (round to the nearest tenth)

Standard Deviation____________________(round to the nearest tenth)

What should the value of the standard deviation be?

Heights of men on a baseball team have a bell shaped distribution with a mean of 185cm and a standard deviation of 8cm. Using the empirical rule, what is the approximate percentage of the men between the following values?

1. 177cm and 193cm
2. 169cm and 201cm

% of men that are between 177 and 193cm

% of men that are between 169 and 201cm

Heights of women have a bell shaped distribution with a mean of 158cm and a standard deviation of 7cm. Using the Chebyshev’s theorem, what do we know about the percentage of women with heights that are within 3 standard deviations of the mean? What are the minimum and maximum heights that are within 3 standard deviations of the mean?

At least % of women have heights within 3 standard deviations of 158cm.(round to the nearest percent)

The minimum height _____________

The maximum height________________

The table list probabilities for the corresponding numbers of girls in three births. What is the random variable, what are the possible values, and are its values numerical?

Number of girls XP(x)

00.125

10.375

20.375

30.125

Ted is not particularly creative. He uses the pickup line “If I could rearrange the alphabet I would put U and I together.” The random variable x is the number of girls Ted approaches before encountering one who reacts positively. Determine whether the table describes a probability distribution. If it does, find its mean and standard deviation.

XP(x)

10.002

20.025

30.128

40.206

50.485

Mean (round to one decimal place)

Standard deviation (round to one decimal place)

Fifteen peas are generated from parents having the green/yellow pair of genes, so there is a 0.75 probability that an individual pea will have a green pod. Find the probability that among the 15 offspring peas, no more than 1 has a green pod. Is it unusual to get more than 1 pea with a green pod when 15 offspring peas are generated? Why or Why not?

The probability that no more than 1 of the 15 offspring peas has a green pod is?(round to three decimal places)

Is it unusual to randomly select 15 peas and find that no more than 1 of them have a green pod? Note that a small probability is one less than 0.05.

Assume that a procedure yields a binomial distribution with n trials and the probability of success for one trial is p. Use the given values of n and p to find the mean and standard deviation. Also, use the range rule of thumb to find the minimum usual value (mean-2) find the maximum value (mean+2)

N=60, P=0.4

Standard deviation (round to one decimal place)

Minimum and maximum (round to one decimal place)

A headline in a certain newspaper states that “most stay at first job for less than 2 years”. That headline is based on an online poll of 370 college graduates. Among those polled, 84% stayed at their first fulltime job less than 2 years. Complete parts a-d.

Assuming that 50% is the true percentage of graduates who stay at their first job less than 2 years find the mean and standard deviation of such graduates in randomly selected groups of 370 students. (simplify your answer)

Assuming that the answer in part A is correct find the range of usual values of graduates who stay at their first job less than 2 years. (the number falls between ______ and _______ use ascending order and round to one decimal place as needed.)

1. Find the actual number of surveyed graduates who stayed at their first job less than 2 years . Use the range of values from part b to determine whether that number is unusual. Does the result suggest that the headline is not justified? (round to the nearest whole number)
2. Is the actual number of graduates who stayed at their first job less than 2 years unusual?

A. for classes of 270 students, find the mean and the standard deviation for the number born on the fourth of July. Ignore leap years

For a class of 270 students would 2 be an unusually high number who were born on the 4th of July?

The value of the mean __________ (round to six decimal places)

The value of the standard deviation ____________ (round to six decimal places)