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A study of smartphone users found that 70% password protect their device. Suppose 15 smartphone users...

  1. A study of smartphone users found that 70% password protect their device. Suppose 15 smartphone users are selected at random.

    1. a) Define the random variable of interest, X.

    2. b) State the distribution of X. Show your work by checking the relevant criteria.

    3. c) What is the probability that exactly 10 password protect their device?

    4. d) What is the probability that more than 11 password protect their device?

    5. e) What is the probability that between (inclusive) 2 and 13 password protect their device?

    6. f) Determine the variance of X.

math   Statistics-And-Probability   
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Answer #1

From the information, observe that a study of smart phone users found that 70% password protect their device The number of smart phones is 15. a) The random variable of interest Xis the number of smart phone users who are protecting their device with the password. b) The distribution of Xis Binomial distribution because the number of smart phone users is finite and independently protecting their phone with the password and the probability of protecting their device with password is fixed for every user. That is, X ~ Bin(n= 15, p=0.70)c) Calculate the probability that exactly 10 password protect their device 15 10 0.70) (1-0.70) 0 3003 × 0.0282 × 0.0024 0.2061 10 d) Calculate the probability that more than 11 password protect their device P(X>11) 1- P(Xs11) 1-(-BIONDIST(11,15,07,TRUE)) = 1-0.7031 0.2969Calculate the probability that between 2 and 13 password protect their device. 13 0.9647-0.0000 = 0.9647 f) Calculate variance of X. V(x)-np(1-p) 15 x 0.7 x 0.3 15x0.21 =3.15

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