Question

A construction company is considering submitting bids for two contracts. The company estimates that it has a 20% chance of winning any given bid. Here is the probability distribution of X = the number of bids the company wins: 0 1 2 X = # of bids won P(X) 0.64 0.32 0.04 Given that u x = 0.4 bids, calculate ox. Round your answer to two decimal places

Answer 1

The standard deviation (ox) for the number of bids won can be calculated using the formula ox = √(npq), where n is the number of trials, p is the probability of success, and q is the probability of failure. In this case, the standard deviation is 0.69 bids.

Step-by-step explanation:

To find the standard deviation (ox), we can use the formula:

ox = √(npq)

Given that the mean (u x) is 0.4 bids, we can calculate ox using the probability distribution provided:

ox = √(2(0.4)(1-0.4)) = √(2(0.4)(0.6)) = √0.48 = 0.69

Therefore, the standard deviation (ox) is 0.69 bids.

Answer 2

To calculate the standard deviation of the number of bids won by a construction company, the variance was found to be 0.32, and the standard deviation was calculated as σx ≈ 0.57 after rounding to two decimal places.

Step-by-step explanation:

The construction company's estimated probability distribution for the number of bids won is given, with a mean of μx = 0.4. To calculate the standard deviation σx, we can use the formula σ = √(σ2), where σ2 is the variance. The variance is calculated as σ2 = E(X2) - (μx)2. We compute E(X2) as follows: E(X2) = (0)(0.64) + (1)2(0.32) + (2)2(0.04) = 0 + 0.32 + 0.16 = 0.48. Now, we can subtract the square of the mean from this value to find variance: σ2 = 0.48 - (0.4)2 = 0.48 - 0.16 = 0.32. Finally, the standard deviation is σx = √(0.32) = 0.57 (rounded to two decimal places).