# Statistics and Probability Homework

Statistics and Probability Homework

3. The accompanying table describes results from groups of 10 births from 10 different sets of parents. The random variable x represents the number of girls among 10 children. Use the range rule of thumb to determine whether 1 girl in 10 births is a significantly low number of girls.

Use the range rule of thumb to identify a range of values that are not significant.

The maximum value in this range is?

(Round to one decimal place as needed.)

6. Assume that when adults with smartphones are randomly selected, 49%

use them in meetings or classes. If 7

adult smartphone users are randomly selected, find the probability that exactly 3

of them use their smartphones in meetings or classes.

The probability is?

(Round to four decimal places as needed.)

7. Assume that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.75

probability that a pea has green pods. Assume that the offspring peas are randomly selected in groups of 20.

Complete parts (a) through (c) below.

a. Find the mean and the standard deviation for the numbers of peas with green pods in the groups of 20.

The value of the mean is μ=?

peas.

(Type an integer or a decimal. Do not round.)

8. When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 40

batteries and determine whether each is within specifications. The entire shipment is accepted if at most 3

batteries do not meet specifications. A shipment contains 7000

batteries, and 3%

of them do not meet specifications. What is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected?

The probability that this whole shipment will be accepted is?

(Round to four decimal places as needed.)

9.If a procedure meets all of the conditions of a binomial distribution except the number of trials is not fixed, then the geometric distribution can be used. The probability of getting the first success on the xth trial is given by P(x)=p(1−p)x−1,

where p is the probability of success on any one trial. Subjects are randomly selected for a health survey. The probability that someone is a universal donor (with group O and type Rh negative blood) is 0.07.

Find the probability that the first subject to be a universal blood donor is the eighth

person selected.

The probability is?

(Round to four decimal places as needed.)

10. A rare form of malignant tumor occurs in 11 children in a million, so its probability is 0.000011. Four cases of this tumor occurred in a certain town, which had 12,800

children.

a. Assuming that this tumor occurs as usual, find the mean number of cases in groups of

12,800

children.

b. Using the unrounded mean from part (a),

find the probability that the number of tumor cases in a group of 12,800

children is 0 or 1.

c. What is the probability of more than one case?

d. Does the cluster of four cases appear to be attributable to random chance? Why or why not?

a. The mean number of cases is?

(Type an integer or decimal rounded to three decimal places as needed.)

11. Match these values of r with the accompanying scatterplots: 0.994,

−0.697,

−0.994,

−1,

and 0.352.

Match the values of r to the scatterplots.

Scatterplot 1, r=▼

Scatterplot 2, r=▼

negative 0.994−0.994

negative 0.697−0.697

0.3520.352

negative 1−1

0.9940.994

Scatterplot 3, r=▼

0.3520.352

0.9940.994

negative 1−1

negative 0.697−0.697

negative 0.994−0.994

Scatterplot 4, r=▼

negative 0.697−0.697

negative 1−1

negative 0.994−0.994

0.3520.352

0.9940.994

Scatterplot 5, r=▼

0.3520.352

negative 0.697−0.697

negative 1−1

negative 0.994−0.994

0.994

13. Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 139 to 189 cm and weights of 41 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x=167.65 cm, y=81.63 kg, r=0.277, P-value=0.005, and y=−105+1.01x. Find the best predicted value of y (weight) given an adult male who is 141 cm tall. Use a 0.10 significance level.The best predicted value of y for an adult male who is 141 cm tall is?

kg.(Round to two decimal places as needed.)

14. a. Using the pairs of values for all 10 points, find the equation of the regression line.b. After removing the point with coordinates (1,4), use the pairs of values for the remaining 9 points and find the equation of the regression line.c. Compare the results from parts (a) and (b).02468100246810xy

A scatterplot has a horizontal x-scale from 0 to 10 in increments of 1 and vertical y-scale from 0 to 10 in increments of 1. Ten points are plotted with nine points, (3, 7), (4, 7), (5, 7), (3, 8), (4, 8), (4, 8), (5, 8), (3, 9), (4, 9), and (5, 9), forming a square and the tenth point (1, 4) being below and to the left of the square.a. What is the equation of the regression line for all 10 points?y=?+?x (Round to three decimal places as needed.)

Statistics and Probability Homework

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Statistics and Probability Homework