Hi please review my homework and see if the question I answered are correct and help with 3 questions that are left unanswered in simple typing terms

Thank you

Professor Michael used his previous year's attendance records from her statistics class of 32 students to construct the following probability distribution.The table lists the number of people absent on an exam day and its assigned probability.

X P(X)

1 0.15

2 0.25

3 0.2

4 0.15

5 0.05

6 0.1

7 0.05

8 0.05

a)What is the probability that between 3 and 5 students, inclusive, are absent on exam day?

Answer

0.2 + 0.15 +0.05 = 0.4

b)On average how many students would you expect to be absent on an exam day?

Answer

1x 0.15 + 2 x 0.25 + 3x 0.2 + 4x 0.15 + 5x 0.05 + 7x 0.05 + 8x 0.05=

0.15 + 0.5 + 0.6 + 0.25 +0.6 + 0.35 + 0.04 = 3.45

A recent report shows that 80% of elementary school teachers have a computer at home.12 elementary school teachers are randomly selected.You may assume this situation follows a binomial distribution.Find the probability that at most 6 of them have a home computer. ?

Please explain in easy steps

A software company sells software on the Internet.The number of unsolicited sales follows a Poisson distribution with a mean of 5 sales per day.What is the probability the company makes at least 1 sale in one day?

Please explain in easy steps

According to the 1998 Health and Human Service's National Household Survey on Drug Abuse, 18% of children between the ages of 12 and 17 are cigarette smokers.If 8 children in this age group are selected randomly find the probability that 2 of them are cigarette smokers.You may assume this is a binomial probability.

Answer

The binomial distribution formula;

p =1/8

q = 7/8

r = 2

n = 8

Therefore the probability that 2 of the children are cigarette smokers =0.1963

According to the manufacturer of Crackle natural peach-flavored iced tea drinks, the net amount of iced tea in a glass bottle is normally distributed with a mean of 12 ounces and a standard deviation of 0.018 ounces.You randomly select one bottle of iced tea this company produced.You may assume this situation is normally distributed.

a)What is the probability that it has less than 11.98 ounces in it?

Answer

x = <11.98

= 12

= 0.018

z = (11.98 - 12)/(0.018)

z = -1.11

P (x < 11.98) = P (z < -1.11) = 0.1335

b)What is the probability that it has between 11.96 ounces and 12.02 ounces, inclusive, in it?

x = 11.96

= 12

= 0.018

z = (11.96 - 12)/(0.018)

z = -2.22

p-value for z = -2.22 in the z-table.

P (x < 11.96) = P (z < -2.22) = 0.0132

z = (12.02 - 12)/(0.018)

z = 1.11

p-value for z = 1.11 in the z-table.

P (x < 12.02) = P (z < 1.11) = 0.8665

P (11.96 -2.22) = 0.8665 - 0.0132 = 0.8533

It is claimed that 25% of Americans have cellular phones.A survey of 440 Americans is conducted. You may assume this binomial distribution is approximately normally distributed.a) Calculate the mean and standard deviation of this distribution.

Answer

1n = 440

p = 25% = 25/100 = 0.25

q = 1 - 0.25 = 0.75

Mean = np

Mean = (440)(0.25)

Mean = 110

Standard deviation = sqrt(440 * 0.25 * 0.75)

Standard deviation = sqrt (82.5)

Standard deviation = 9.083

The heights of 12-month-old boys are approximately normally distributed with a mean of 29.8 inches and a standard deviation of 1.2 inches.

Please explain this answer in easy steps

a)What height separates the shortest 20% of 12-month-old boys from the rest?

b)What height separates the tallest 30% of 12-month-old boys from the rest?

According to the 1998 Health and Human Service's National Household Survey on Drug Abuse, 18% of children between the ages of 12 and 17 are cigarette smokers.If 8 children in this age group are selected randomly find the probability that 2 of them are cigarette smokers.You may assume this is a binomial probability.

Answer

The binomial distribution formula;

p =1/8

q = 7/8

r = 2

n = 8

Therefore the probability that 2 of the children are cigarette smokers =0.1963