Question

In: Math

The distribution of the number of viewers for the American Idol television show follows a normal...

The distribution of the number of viewers for the American Idol television show follows a normal distribution with a mean of 29 million with a standard deviation of 6 million.

What is the probability next week's show will:

Have between 32 and 41 million viewers? (Round your z-score computation to 2 decimal places and final answer to 4 decimal places.)
Have at least 24 million viewers? (Round your z-score computation to 2 decimal places and final answer to 4 decimal places.)
Exceed 46 million viewers? (Round your z-score computation to 2 decimal places and final answer to 4 decimal places.)

Solutions

Expert Solution

Let "X" be the number of viewers for the American Idol television.

Refer Z-table to find the probability or use excel formula "=NORM.S.DIST(2.00, TRUE)" & "=NORM.S.DIST(0.50, TRUE)" to find the probability.

--------------------------------------------------------------------------------------------------------

Refer Z-table to find the probability or use excel formula "=NORM.S.DIST(-1, TRUE)" to find the probability.

--------------------------------------------------------------------------------------------------------

Refer Z-table to find the probability or use excel formula "=NORM.S.DIST(2.83, TRUE)" to find the probability.

milcah answered 8 months ago

Next > < Previous

Related Solutions

The distribution of the number of viewers for the American Idol television show follows a normal...

The distribution of the number of viewers for the American Idol television show follows a normal distribution with a mean of 26 million with a standard deviation of 8 million. What is the probability next week's show will: a. Have between 30 and 37 million viewers? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) b. Have at least 21 million viewers? (Round z-score computation to 2 decimal places and your final answer to...

The distribution of the number of viewers for the American Idol television show follows a normal...

The distribution of the number of viewers for the American Idol television show follows a normal distribution with a mean of 32 million with a standard deviation of 6 million. What is the probability next week's show will: Have between 38 and 44 million viewers? (Round your z-score computation to 2 decimal places and final answer to 4 decimal places.) Have at least 23 million viewers? (Round your z-score computation to 2 decimal places and final answer to 4 decimal...

The distribution of the number of viewers for the American Idol television show follows a normal...

The distribution of the number of viewers for the American Idol television show follows a normal distribution with a mean of 32 million with a standard deviation of 4 million. What is the probability next week's show will: Have between 36 and 43 million viewers? (Round your z-score computation to 2 decimal places and final answer to 4 decimal places.) Have at least 29 million viewers? (Round your z-score computation to 2 decimal places and final answer to 4 decimal...

The number of viewers of American Idol has a mean of 29 million with a standard...

The number of viewers of American Idol has a mean of 29 million with a standard deviation of 4 million. Assume this distribution follows a normal distribution. What is the probability that next week's show will: (a) Have between 31 and 38 million viewers? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Probability (b) Have at least 20 million viewers? (Round z-score computation to 2 decimal places and...

Lucy Baker is analyzing demographic characteristics of two television programs, American Idol (population 1) and 60...

Lucy Baker is analyzing demographic characteristics of two television programs, American Idol (population 1) and 60 Minutes (population 2). Previous studies indicate no difference in the ages of the two audiences. (The mean age of each audience is the same.) Her staff randomly selected 100 people from each audience, and reported the following: sample mean for population 1 = 43 years and sample mean for population 2 = 45 years. Assume that σ 1 = 5 and σ 2 =...

A recent sports game set a record for the number of television viewers. The game had...

A recent sports game set a record for the number of television viewers. The game had a share of 78%, meaning that among the television sets in use at the time of the game, 78% were tuned to the game. The sample size is 25,563 households. Use a 0.01 significance level to test the claim that more than 74%of television sets in use were tuned to the sports game. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about...

The number of plants pollinated by bees follows a normal distribution with a mean of 6,543...

The number of plants pollinated by bees follows a normal distribution with a mean of 6,543 plants pollinated a day with a standard deviation of 35 plants per day. What is the probability that between 6,500 and 6,530 plants were pollinated? Group of answer choices 0.1654 0.2464 0.2501 0.465

It is known that 40% of American Idol winners become famous. A sample of 50 American...

It is known that 40% of American Idol winners become famous. A sample of 50 American Idol winners are randomly selected. (a) [1] What is the probability that exactly 25 of them become famous? (b) [1] Find the probability that at least 20 of them become famous. (c) [2] What is the probability that between 17 and 27 (including both 17 and 27) of them become famous. (d) [2] Find the expected number of American Idol winners become famous in...

The distribution of ages of all the employees in Company X follows a normal distribution. The...

The distribution of ages of all the employees in Company X follows a normal distribution. The average age is 40 and the standard deviation is 5. Find the Z-score of a 50 year old employee. What is the probability that a randomly chosen employee will be younger than 35 years? What is the probability that a randomly chosen employee will have an age between 35 and 45 years? What is the probability that a randomly chosen employee will be older...

The diameter of a cylinder follows a normal distribution with the mean of 10cm and the...

The diameter of a cylinder follows a normal distribution with the mean of 10cm and the variance of 0.04 cm^2. a) Construct a Shewhart chart to monitor the process mean of cylinder diameter with a sample size 9? (Use L=3) b) If the mean of the process changes to 10.5 cm, what is the probability that you detect this mean shift at the immediate next sample (the first sample after the mean shift)? c) Continue b), what is the probability...

Subjects