If 15% of children in France play video games, what is the probability that fewer than...

If 15% of children in France play video games, what is the probability that fewer than 54 out of a random sample of 450 adults will play video games?

(round answer to nearest 3 decimal places)

Solutions

Expert Solution

Probability of playing video games = p = 0.15 (15%=0.15)

Random Sample Size = n = 450

We will use Normal approximation to Binomial distribution in this case as sample size is quite large.

Let X denotes number of adults who play video games in the sample.

Mean = np = 450*0.15 = 67.5

Standard Deviation = = 7.575

We have to find the probability that fewer than 54 out of a random sample of 450 adults will play video games

i.e.

We get the phi value from Normal z table(attached).

The probability that fewer than 54 out of a random sample of 450 adults will play video games is 0.037

z table :

orchestra answered 1 year ago

Next > < Previous

Related Solutions

(15 marks) Diana's kids, Naomi and Isaac, play a lot of video games together. On a...

Diana's kids, Naomi and Isaac, play a lot of video games together. On a particular level, the number of points Naomi scores has a Discrete Uniform distribution on [5,11] and the number of points Isaac scores has a Discrete Uniform distribution on [6, 9]. Each time they play, their scores are independent. (a) (2) Write down an expression for the probability that in 100 games, the total number of points scored by Naomi and Isaac is at least 1600. Do...

The effects of video games on the cognitive development of children

If 10% of the general population smokes, what is the approximate probability that fewer than 100...

If 10% of the general population smokes, what is the approximate probability that fewer than 100 in a random sample of 928 people are smoker?

It has been reported that 48% of teenagers play video games on their phones. A random...

It has been reported that 48% of teenagers play video games on their phones. A random sample of 60 teenages is drawn. Find the probability that the proportion of teenagers in the sample who play videos games on their phone is less than 0.500 . Write only a number as your answer. Round to 4 decimal places (for example 0.3748). Do not write as a percentage.

Diana's kids, Naomi and Isaac, play a lot of video games together. On a particular level,...

Diana's kids, Naomi and Isaac, play a lot of video games together. On a particular level, the number of points Naomi scores has a Discrete Uniform distribution on [6,12] and the number of points Isaac scores has a Discrete Uniform distribution on [7, 10]. Each time they play, their scores are independent. (a) (2) Write down an expression for the probability that in 100 games, the total number of points scored by Naomi and Isaac is at least 1800. Do...

Suppose Bethany buys both CDs and video games. The price of a CD is $15 and the price of a video game is $30.

Suppose Bethany buys both CDs and video games. The price of a CD is $15 and the price of a video game is $30. Suppose that given Bethany’s planned expenditures, she receives 900 utils from her last planned purchase of CDs and 1,200 utils from her last planned purchase of video games. Is she at the optimal combination of CDs and video games? Explain. If not, explain how she should alter her consumption bundle. (Hint: use Marginal utilities and prices...

Gamers are described as people who regularly play video games. A random sample of 80 people...

Gamers are described as people who regularly play video games. A random sample of 80 people were selected and found 50 to be mail. The 99% confidence interval for the proportion based on the sample is

USING EXCEL: Consider the probability that no fewer than 75 out of 111 houses will lose...

USING EXCEL: Consider the probability that no fewer than 75 out of 111 houses will lose power once a year. Assume the probability that a given house will lose power once a year is 98% Specify whether the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions. PLEASE USE EXCEL AND SHOW EXCEL FORMULAS USED FOR SOLUTION. THANK YOU!!

Consider the probability that fewer than 19 out of 156 people have been in a car...

Consider the probability that fewer than 19 out of 156 people have been in a car accident. Assume the probability that a given person has been in a car accident is 8%. Aprroximate the probability using the normal distribution. Round your answer to four decimal places. Need answer ASAP thanks!

Calculate each binomial probability: (a) Fewer than 4 successes in 9 trials with a 10...

Calculate each binomial probability: (a) Fewer than 4 successes in 9 trials with a 10 percent chance of success. (Round your answer to 4 decimal places.) Probability (b) At least 1 successe in 5 trials with a 10 percent chance of success. (Round your answer to 4 decimal places.) Probability (c) At most 11 successes in 19 trials with a 70 percent chance of success. (Round your answer to 4 decimal places.) ...

Subjects