Question

1. A normal distribution has a mean of 105.0 and a standard deviation of 18.0. Calculate the Z score that you would use in order to find the probability P(X>111.0)

2. A statistical experiment involves recording the number of times a light blinks during intervals of varied durations. Historically, the light blinks at a rate of 5.1 times per minute on average. Calculate the probability that in a randomly selected 5.5-minute interval, the light blinks 31 times.

3. Consider a binomially distributed random variable constructed from a series of 8 trials with a 60% chance of success on any given trial. Calculate the probability that there are more than 3 successes.

4. A statistical experiment involves conducting 16 independent trials where each trial has only two possible and mutually exclusive outcomes. The probability that outcome A occurs in any given trial is 0.57. Calculate the likelihood that outcome A occurs 12 times in the experiment.

Enter your response as a decimal rounded to 3 places. For example, if you think the answer is 20.4%, then enter 0.204 into the blank below.

5. A box contains 4 red balls, 3 yellow balls, and 3 green balls. You will reach into the box and blindly select a ball, take it out, and then place it to one side. You will then repeat the experiment, without putting the first ball back. Calculate the probability that the two balls you selected include a yellow one and a green one.

6. A box contains 3 red balls, 3 yellow balls, and 2 green balls. You will reach into the box and blindly select a ball, take it out, and then place it to one side. You will then repeat the experiment, without putting the first ball back. Calculate the probability that you selected a yellow ball on the first draw and then a green one on the second draw.

Answer 1

Note:

Since you have asked multiple questions, we will solve the first question for you. If you want any specific question to be solved then please specify the question number or post only that question.

1)

Given:

Population mean = μ=105

Population standard deviation = σ=18

We have to find P(X>111) = ...?

Z-score = 0.3333

P(Z>0.3333)=1-P(Z<0.3333)

P(Z>0.3333) =1−0.6306=0.3694  ...Using excel formula, =NORMSDIST(0.3333)

Hence,

P(X>111) = 0.3694

Done