Questions: Market-share-analysis company Net Applications monitors and reports on Internet browser usage. According to Net Applications, in the summer of 2014, Google's Chrome browser exceeded a 20% market share for the first time, with a 20.37% share of the browser market (Forbes website). For a randomly selected group of 20 Internet browser users, answer the following questions. a. Compute the probability that exactly 8 of the 20 Internet browser users use Chrome as their Internet browser (to 4 decimals). b. Compute the probability that at least 3 of the 20 Internet browser users use Chrome as their Internet browser (to 4 decimals). c. For the sample of 20 Internet browser users, compute the expected number of Chrome users (to 3 decimals). d. For the sample of 20 Internet browser users, compute the variance and standard deviation for the number of Chrome users (to 3 decimals). Variance Standard deviation

Market-share-analysis company Net Applications monitors and reports on Internet browser usage. According to Net Applications, in the summer of 2014, Google's Chrome browser exceeded a 20% market share for the first time, with a 20.37% share of the browser market (Forbes website). For a randomly selected group of 20 Internet browser users, answer the following questions. a. Compute the probability that exactly 8 of the 20 Internet browser users use Chrome as their Internet browser (to 4 decimals). b. Compute the probability that at least 3 of the 20 Internet browser users use Chrome as their Internet browser (to 4 decimals). c. For the sample of 20 Internet browser users, compute the expected number of Chrome users (to 3 decimals). d. For the sample of 20 Internet browser users, compute the variance and standard deviation for the number of Chrome users (to 3 decimals). Variance Standard deviation
Transcript text: Market-share-analysis company Net Applications monitors and reports on Internet browser usage. According to Net Applications, in the summer of 2014, Google's Chrome browser exceeded a $20 \%$ market share for the first time, with a $20.37 \%$ share of the browser market (Forbes website). For a randomly selected group of 20 Internet browser users, answer the following questions. a. Compute the probability that exactly 8 of the 20 Internet browser users use Chrome as their Internet browser (to 4 decimals). For this question, if you compute the probability manually, make sure to carry at least six decimal digits in your calculations. $\square$ b. Compute the probability that at least 3 of the 20 Internet browser users use Chrome as their Internet browser (to 4 decimals). $\square$ c. For the sample of 20 Internet browser users, compute the expected number of Chrome users (to 3 decimals). $\square$ d. For the sample of 20 Internet browser users, compute the variance and standard deviation for the number of Chrome users (to 3 decimals). Variance $\square$ Standard deviation $\square$
failed

Solution

failed
failed

Solution Steps

Hint

To solve these types of problems, use the binomial probability formula for calculating the likelihood of a specific number of successes in a series of independent trials. For cumulative probabilities, sum the probabilities of the desired range of outcomes or subtract the probabilities of the complement from one. The expected value and variance are found using the formulas for a binomial distribution, and the standard deviation is the square root of the variance.

Step 1: Compute the probability that exactly 8 of the 20 Internet browser users use Chrome

To find the probability that exactly 8 out of 20 users use Chrome, we use the binomial probability formula:

\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \]

Given:

  • \( n = 20 \)
  • \( p = 0.2037 \)
  • \( k = 8 \)

The probability is:

\[ P(X = 8) \approx 0.0243 \]

Step 2: Compute the probability that at least 3 of the 20 Internet browser users use Chrome

To find the probability that at least 3 out of 20 users use Chrome, we calculate the cumulative probability for \( X \) being less than 3 and subtract it from 1:

\[ P(X \geq 3) = 1 - P(X < 3) \]

The probability is:

\[ P(X \geq 3) \approx 0.8051 \]

Step 3: Compute the expected number of Chrome users

The expected number of Chrome users in a sample of 20 is given by the formula for the expected value of a binomial distribution:

\[ E(X) = n \cdot p \]

Given:

  • \( n = 20 \)
  • \( p = 0.2037 \)

The expected value is:

\[ E(X) = 20 \cdot 0.2037 = 4.074 \]

Step 4: Compute the variance and standard deviation for the number of Chrome users

The variance of a binomial distribution is given by:

\[ \text{Var}(X) = n \cdot p \cdot (1 - p) \]

The standard deviation is the square root of the variance:

\[ \sigma = \sqrt{\text{Var}(X)} \]

Given:

  • \( n = 20 \)
  • \( p = 0.2037 \)

The variance is:

\[ \text{Var}(X) = 20 \cdot 0.2037 \cdot (1 - 0.2037) \approx 3.244 \]

The standard deviation is:

\[ \sigma \approx 1.801 \]

Final Answer

\[ \boxed{P(X = 8) \approx 0.0243} \] \[ \boxed{P(X \geq 3) \approx 0.8051} \] \[ \boxed{E(X) = 4.074} \] \[ \boxed{\text{Var}(X) \approx 3.244} \] \[ \boxed{\sigma \approx 1.801} \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Module 06 Homework Question 11 of 13 (1 point) Question Attempt: 1 of Unlimited Incorrect You've picked the wrong sketch in all cases. There are three sets of sketches below, showing the same pure molecular compound (water, molecular formula H2O) at three different temperatures. The sketches are drawn as if a sample of water were under a microscope so powerful that individual atoms could be seen. Only one sketch in each set is correct. Use the slider to choose the correct sketch in each set. You may need the following information: melting point of H2O: 0.0°C boiling point of H2O: 100.0°C
failedAnswered
approaches, but does not touch, the -axis.
failedAnswered
Which of the following is classified as a plant asset? Multiple Choice Equipment Accounts receivable. Cash. Supplies. Merchandise inventory.
failedAnswered
Student 1 114 132 79 24 30 18 student 2 92 130 67 17 22 13 student 3 90 b / m 102 b / m 60 b / m 54 b / m 90 b / m 24 b / m student 4 72 140 60 30 70 16 student 5 90 120 95 25 28 18 bpm student 6 420 456 96 300 325 150 student 7 102 132 82 66 78 38 student 8 188 210 48 210 230 120 breaths student 9 140 beats 288 beats 67 beats 60 breaths 96 breaths 32 breaths student 10 95 117 64.33 23 29 13.33 student 11 119 97 105 28 40 15 student 12 82 80 81 16 18 17 student 13 114 140 78 50 70 26 student 14 74 72 72 7 7 7 student 15 104 115 87 29 32 21 student 16 72 150 42 36 54 28 student 17 72 164 62 52 98 47 student 18 103 bpm 113 bpm 73 bpm 21 b / m 47 b / m 16 b / m student 19 80 88 85.33 19 18 18.33 student 20 112 BPM 126 BPM 58.3 BPM 14 BPM 16 BPM 11.7 BPM student 21 109 128 87 28 37 14 student 22 68 76 61.3 19 20 13 student 23 128 132 85 11 11 9 student 24 124 130 81.6 20 42 12.6 student 25 102 121 78 34 39 19 student 26 115 bpm 132 bpm 81.33 24 31 17.66 student 27 88 112 74.66 39 56 27.33 student 28 106 124 77.3 25 41 12 student 29 149 151 97.33 41 43 17.67 student 30 100 114 58.7 22 26 13.3 student 31 72 108 68 24 35 15 student 32 82 89 79 26 30 21 student 33 105 91 105 30 17 30 student 34 112 116 65.3 11 18 8.3 student 35 144 160 100 22 25 15 student 36 79 75 66 20 25 16 student 37 84 71 42 25 30 11.3 student 38 90 80 21 25 20 18 student 39 126 144 87 35 46 19 student 40 88 76 69.33 13 11 9.67
failedAnswered
Solve for y. 5y/4 + 3 = 7y/6 Simplify your answer as much as possible. y=