Need help number 1 and 2 showing details omi apu your answers to the following q

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Need help number 1 and 2 showing details



omi apu your answers to the following questions and type up in a Microsoft WORD Document. ALL ANSWERS BELOW WILL REQUIRE YOU TO SHO DETAILED CALCULATIONS FOR EVERY ANSWER THAT YOU PROVIDE. IF NO DETAILED CALCULATIONS ARE PROVIDED AND A LISTED, YOU WILL NOT RECEIVE ANY POINTS FOR THAT ANSWER TO THE PROBLEMI!! As always, once completed you will upload this 1. A psychology class consists of 14 males and 36 females. f the professor selects names from the class ist using random sampling a. What is the probability that the first student selected will be a female? (12.5 points) b. If a random sample of n 3 students is selected and the first two are both females, what is the probability that the third student selected will be a male? (12.5 points) to a recent report, people smile an average of u - 62 times per day, Assuming that the distribution of smiles is approximately normal with a standard deviation of : 18, find each of the following values: a. What proportion of people smile more than 80 times a-day? (12.5 points) b. what proportion of people smile at least 50 times a day? (12.5 points) information from the Department of Motor Vehicles Indicates that the average age of licensed drivers is :457 years with a standard deviation of 12.5 yeirs Assum ng that the distribution of rivers ages is approxi mately normal, answer the following questions a. What proportion of licensed drivers are older than 50 years old? (12.5 points) b Whet propörtion of licensed drivers are younger than s0 vears old? (12 5 points) port in 2010 indicates that Americans between the ages of 8 and 18 spend an average of u-7.5 ours per day using some sort of electronic device such as smärt phones, computers, or tablets. Assume that the distribution of times is normal with a standard deviation of o a 2.5 hours and find the following values is the probability of selecting an individual who uses electronic devices more than 12 hours a day? points) proportio ept the less tnan symbol SHOULD NOT HAV E THE UNDER LI NE MAKING IT LESS THAN OR EOUAL TO ¡couldnt edit the s to 1e year-old Americans spend between s and 10 hours per day using electronic devices in symbols it would look ou ment te zet rid of the line underneath, so the symbol n should just say p5 ess than X less than I (ie, p/5 s xs 10-2(125

Explanation / Answer

1)
a)
Female student can be selected in 36C1 ways
Required probability = 36/50 = 0.72

b)
The third student can either be female or male, probability = (36C1*35C1*14C1 + 36C1*35C1*34C1)/(50C1*49C1*48C1) = 0.5143

probability that the third student selected in male = 36C1*35C1*34C1/(50C1*49C1*48C1) = 0.15

Hence required probability = 0.15/0.5143 = 0.2917

2)
mean = 62 , s = 18
a)
P(x >80)
z = (x - mean) / s
= ( 80 -62)/18
= 1

P(x >80) = P(z >1) = 0.1587 by using z standard normal table

b)

P(x >50)
z = (x - mean) / s
= ( 50 -62)/18
= -0.667

P(x >50) = P(z >-0.667) =0.7475 by using z standard normal table

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