PhD’s in Engineering. The National Science Foundation reports that 70% of the U. S. graduate students who earn PhD degrees in engineering are foreign nationals. Consider the number Y of foreign students in a random sample of 25 engineering students who recently earned their PhD. a) Find the probability that there are exactly 10 foreign students in your sample – use equation for thisb) Find the probability that there are less than or equal to 5 foreign students in your sample andc) Find the mean and standard deviation for Y

a) P(Y=10)=0.0013

b) P(Y≤5)=0.00000035

c) Mean = 17.5

S.D. = 2.29

Step-by-step explanation:

We can model this as a binomial random variable with n=25 and p=0.7.

The probability that k students from the sample are foreign students can be calculated as:

a) Then, for Y=10, the probability is:

b) We have to calculate the probability P(Y≤5)

c) The mean and standard deviation for this binomial distribution can be calculated as:

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step-by-step explanation:

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