Homework: Section 6.5 Homework HW Score: 50%, 6 of Score: 0 of 1 pt 2 of 12 (6 c

Question

Homework: Section 6.5 Homework HW Score: 50%, 6 of Score: 0 of 1 pt 2 of 12 (6 complete) Question Help 6.5.5 Assume that women's heights are normally distributed with a mean given by -641 in, and a standard deviation given by ?-2 8 in (a) If 1 woman is randomly selected, find the probability that her height is less than 65 in (b) If 35 women are randomly selected, find the probability that they have a mean height less than 65 in (a) The probability is approximately co (Round to four decimal places as needed.) mis (MAT 2018 P Enter your answer in the answer box and then click Check Answer Check Clear All part remaining

Explanation / Answer

Solution:- Given that mean µ = 64.1 in?, standard deviation ? = 2.8 in.

(?a) The probability is approximately 0.6255.

=> P(X < 65) = P(Z < (65 – 64.1) ÷ 2.8)

= 0.3214

P ( Z < 0.3214 ) = 0.6255

Area to the left of z = 0.3214 is approximately 0.6255

(b) The probability is approximately 0.9713.

?x? = ? ÷ ?(n)

= 2.8 ÷ ?(35)

= 0.4733

=> P(X < 65) = P(Z < (65 – 64.1) ÷ (2.8 ÷ ?(35)))

= 1.9016

P ( Z < 1.9016 ) = 0.9713

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