Question

A) The distribution of exam scores for Statistics is normally distributed with a mean of 78 and a standard deviation of 5.2. What is the z-score for a raw score of 85? Round to the nearest hundredth.

B) An Olympic archer is able to hit the bull’s eye 80% of the time. Assume each shot is independent of the others. She will shoot 6 arrows. Let X denote the number of bull’s eyes she makes.

Find the standard deviation of the probability distribution of X. Round to the nearest hundredth.

C) An Olympic archer is able to hit the bull’s eye 80% of the time. Assume each shot is independent of the others. She will shoot 6 arrows. Let X denote the number of bull’s eyes she makes.

What is the probability that she gets at least four bull’s eyes? Round to four decimal places.

Answer 1

Answer:

A)

=  78, = 5.2, x= 85

formula for z-score is

z = 1.346

z-score is = 1.35

B)

P= 80% = 0.8, n=6

formula for Standard deviation of binomial distribution is

= 0.9798

Standard deviation= 0.98

c)

we want to find P(x 4)

formula is

P(x) = nCx * Px * ( 1 - p )n-x

P(x 4) = P(X=4)+P(X=5)+P(X=6)

P(x 4) = 6C4 * 0.84 * ( 1 -0.8)6-4  + 6C5 * 0.85 * ( 1 -0.8)6-5 + 6C6 * 0.86 * ( 1 -0.8)6-6

P(x 4) =0.2458 + 0.3932 + 0.2621

P(x 4) = 0.9011

Probability =  0.9011