Statistics and Probability Answers

Find the mean of the set 7 10 14 17 20 of data and construct a sampling distribution by selecting 3 samples at a time

What is the probability that the shelf life of the

battery is between 500 and 550 days?

1.      Find the range, the standard deviation, and the variance for the given samples. Round noninteger results to the nearest tenth.

       a. 1, 2, 5, 7, 8, 19, 22

       b. 3, 4, 7, 11, 12, 12, 15, 16

       c. 2.1, 3.0, 1.9, 1.5, 4.8

       d. 5.2, 11.7, 19.1, 3.7, 8.2, 16.3

       e. 48, 91, 87, 93, 59, 68, 92, 100, 81

Suppose the amount of a popular sport drink in bottles leaving the filling machine has a normal distribution with mean 101.5 milliliters (mL) and standard deviation 1.6. If 36 bottles are randomly selected, find the probability that the mean content is less than 102.1 mL 

According to a National Health Survey, American men’s heights are normally distributed with a mean given by 𝜇 = 69.7 inches and a standard deviation given by 𝜎 = 2.8 inches.

a). If a man is randomly selected, find the probability that his height is more 72 inches.

b). If a man is randomly selected, find the probability that his height is between 68 and 72 inches.

Suppose that 9 good fuses and 4 defective ones have been mixed up. To find the defective fuses, we test them one-by-one, at random. What is the probability that we are lucky and find both of the defective fuses in the first two tests?

1). With replacement

2). Without replacement

The number of violent crimes committed in a day possesses a distribution with a mean of 2.8 crimes per day and a standard deviation of 4 crimes per day. A random sample of 100 days was observed, and the sample mean number of crimes for the sample was calculated. Describe the sampling distribution of the sample means.

a.) shape unknown with mean of 2.8 and a standard deviation of 0.4

b.) approximately normal with mean of 2.8 and standard deviation of 4

c.) shape unknown with mean of 2.8 and standard deviation of 4

d.) approximately normal with mean of 2.8 and standard deviation of 0.4.

Which one of the following charts represents a probability distribution?

a)

X | P(x)

 0 | 0.1

 1 | 0.2

 2 | 0.4

 3 |  0.1

b)

 X | P(x)

 0 | 0.3

 1 | 0.2

 2 | 0.1

 3 | 0.35

c)

 X | P(x)

 0 | -0.1

 1 | 0.1

 2 | 0.4

 3 | 0.6

d)

 X | P(x)

 0 | 0

 1 | 0

 2 | 1

 3 | 0

1) Newborn babies are more likely to be boys than girls. A random sample found that 13,173 boys were born among 25,468 newborn children. The sample proportion of boys was 0.5172. Is this sample evidence that the birth of boys is more common than the birth of girls in the entire population?

A Jar contains 24 red marbles numbered 1 to 24 and 50 blue marbles numbered 1 to 50. A marble is drawn at random from the Jar. Find the probability of the given event. Please enter reduced fractions.

a) The marble is red. P(red)=

b) The marble is odd numbered. P(odd)=

c) The marble is red or odd numbered. P(red or odd)=

d)The marble is blue or even numbered. P(blue or even)=