Given a standardized normal distribution (with a mean of 0 and a standard deviat

Question

Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1), complete parts (a) through (d).

a. What is the probability that Z is less than 1.08? The probability that Z is less than 1.08 is

.(Round to four decimal places as needed.)

b. What is the probability that Z is greater than 0.23? The probability that Z is greater than 0.23 is

.(Round to four decimal places as needed.)

c. What is the probability that Z is less than 0.23 or greater than the mean? The probability that Z is less than 0.23 or greater than the mean is

.(Round to four decimal places as needed.)

d. What is the probability that Z is less than 0.23 or greater than 1.08?

2. In 2008, the per capita consumption of soft drinks in Country A was reported to be 18.28 gallons. Assume that the per capita consumption of soft drinks in Country A is approximately normally distributed, with a mean of 18.28 gallons and a standard deviation of 5 gallons. Complete parts (a) through (d) below.

a. What is the probability that someone in Country A consumed more than 11 gallons of soft drinks in 2008? The probability is

.(Round to four decimal places as needed.)

b. What is the probability that someone in Country A consumed between 1 and 5 gallons of soft drinks in 2008? The probability is

.(Round to four decimal places as needed.)

c. What is the probability that someone in Country A consumed less than 5 gallons of soft drinks in 2008?

The probability is

.(Round to four decimal places as needed.)

d. 99% of the people in Country A consumed less than how many gallons of soft drinks?

3. According to a social media blog, time spent on a certain social networking website has a mean of 24 minutes per visit. Assume that time spent on the social networking site per visit is normally distributed and that the standard deviation is 4 minutes. Complete parts (a) through (d) below.

a. If you select a random sample of 25 sessions, what is the probability that the sample mean is between

23.5 and 24.5 minutes?

  (Round to three decimal places as needed.)

b. If you select a random sample of 25 sessions, what is the probability that the sample mean is between

23 and 24 minutes?

  (Round to three decimal places as needed.)

c. If you select a random sample of 100 sessions, what is the probability that the sample mean is between

23.5 and 24.5 minutes?

(Round to three decimal places as needed.)

d. Explain the difference in the results of (a) and (c).

The sample size in (c) is greater than the sample size in (a), so the standard error of the mean (or the standard deviation of the sampling distribution) in (c) is

less

greater

than in (a). As the standard error

increases,

decreases,

values become more concentrated around the mean. Therefore, the probability that the sample mean will fall in a region that includes the population mean will always

decrease

increase

when the sample size increases.

4. In a random sample of 76 people, 19 are classified as "successful."

a. Determine the sample proportion, p, of "successful" people.

b. If the population proportion is 0.75 determine the standard error of the proportion.

a.p = (Type an integer or a decimal.)

b. sigma Subscript p= (Round to four decimal places as needed.)

5. A study reports that 36% of companies in Country A have three or more female board directors. Suppose you select a random sample of 100 respondents. Complete parts (a) through (c) below.

a. What is the probability that the sample will have between 32% and 45% of companies in Country A that have three or more female board directors?The probability is

. (Round to four decimal places as needed.)

b. The probability is 90% that the sample percentage of Country A companies having three or more female board directors will be contained within what symmetrical limits of the population percentage?

The probability is 90% that the sample percentage will be contained above

% and below

%.(Round to one decimal place as needed.)

c. The probability is 99.7% that the sample percentage of Country A companies having three or more female board directors will be contained within what symmetrical limits of the population percentage?

The probability is 99.7% that the sample percentage will be contained above

% and below %.(Round to one decimal place as needed.)

Explanation / Answer

As per the Chegg policy, we are advised to do one question at a time so i am attempting the 1st one.

1. From z statistical table, the required probabilities are:

a) P(z < 1.08) = 0.8599

b) P(z > -0.23) = 0.5910

c) P(z < -0.23 or z > 0) = 0.4090 + 0.5 = 0.9090

d) P(z < -0.23 or z > 1.08) = 0.4090 + 0.1401 = 0.5491

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