An exam consists of 50 multiple choice questions. Based on how much you studied, for any given question, you think you have a probability of 0.64 of getting the correct answer. Consider the sampling distribution of the sample proportion of correct questions out of 50. (a) Find the mean and standard error of the sampling distribution of this proportion. Mean = (2 decimal places) Standard error = (3 decimal places) (b) What do you expect for the shape of this sampling distribution? approximately normal because n is large cannot be determined because p is greater than 0.5 cannot be determined because n is large approximately normal because the population is normal (c) If truly p = 0.64, calculate the probability of getting a sample proportion less than 0.60? (correct answers on less than 60% of the questions) Probability = (3 decimal places)

(a) mean = 32.00

(b)Standard error = 0.068

It is expected that the shape will approximately large because n is large.

(c)P(z< 0.60)= 0

Step-by-step explanation:

a. Mean = nP= 0.64× 50 = 32.00(2dp)

P= 0.64

b. Standard error = √ p(1-p)/n

= √0.64(0.36)/50

= 0.068(3dp)

c. Using P(Z<X - U/S)

Where S = standard error

U = mean = 0.64

(c)P(z< 0.60)=

= P( z< 0.60 - 0.64/0.068)

= P( z < -5.88)

= 0.

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.

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