Question

A population of values has a normal distribution with u = 150.7 and o = 14.3. You intend to draw a random sample of size n = 118. Find the probability that a single randomly selected value is between 147.1 and 149.9. P(147.1 < x < 149.9) = Find the probability that a sample of size n = 118 is randomly selected with a mean between 147.1 and 149.9. P(147.1 < M < 149.9) = Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted. License Points possible: 2 This is attempt 1 of 5. Message instructor about this question

Answer 1

Solution :

(a)

P(141.1 < x < 149.9) = P[(141.1 - 150.7)/ 14.3) < (x - $\mu$ ) /$\sigma$  < (149.9 - 150.7) / 14.3) ]

= P(-0.671 < z < )-0.056

= P(z < -0.056) - P(z < -0.671)

= 0.2266

(b)

$\sigma$_{$\bar x$} = $\sigma$ / $\sqrt$ n = 14.3 / $\sqrt$ 118

= P[(147.1 - 150.7) / < 14.3 / $\sqrt$ 118 < ($\bar x$ - $\mu$ _{$\bar x$}) / $\sigma$ _{$\bar x$} < (149.9 - 150.7) / 14.3 / $\sqrt$ 118)]

= P(-4.735 < Z < -0.608)

= P(Z < -0.608) - P(Z < -4.735)

= 0.2716