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Answer: 1.902
## Explanation For a binomial distribution, the standard deviation is calculated as: **Standard Deviation = √[n × p × (1 - p)]** Where: - n = number of trials = 50 companies - p = probability of success (IPO rate) = 7.85% = 0.0785 **Step 1: Calculate the variance** Variance = n × p × (1 - p) = 50 × 0.0785 × (1 - 0.0785) First calculate (1 - p) = 1 - 0.0785 = 0.9215 Then: 50 × 0.0785 = 3.925 3.925 × 0.9215 = 3.616 **Step 2: Calculate the standard deviation** Standard Deviation = √3.616 = 1.9018 ≈ 1.902 **Why other options are incorrect:** - **A (3.616)**: This is the variance, not the standard deviation - **C (1.38)**: This would be the result if using incorrect probability or calculation error - **D (2.125)**: This doesn't match the correct calculation The binomial model is appropriate here because we have a fixed number of independent trials (50 companies), each with the same probability of success (IPO rate of 7.85%), and we're counting the number of successes (IPOs).
Author: Nikitesh Somanthe
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As an investment analyst, your job is to determine how many companies will announce IPOs out of 50 virtual reality startup companies operating in Palo Alto. The annual IPO rate in high-tech industries in all other states of the U.S. is 7.85%. Using a binomial model, what is the standard deviation of the number of virtual reality company IPOs in Palo Alto?
A
3.616
B
1.902
C
1.38
D
2.125