Question

please refer to how you calculate z by graphing calculator

Ind value from Tival Go X Search took hinch + action skip to 5 @ @ Score on last attempt: Score in gradebook: D 0 out of 4 out of 4 0 Try another similar question Question with last attempt is displayed for your review only A particular fruit's weights are normally distributed, with a mean of 673 grams and a standard deviation of 32 grams. If you pick 15 fruit at random, what is the probability that their mean weight will be between 650 grams and 662 grams. 0.0060 Round to 4 decimal places. Answers obtained using exact z-scores or Z-scores rounded to 2 decimal places are accepted. Answer: 0.0888 or 0.0891 DOLL

Answer 1

the PDF of normal distribution is = 1/σ * √2π * e ^ -(x-u)^2/ 2σ^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd/sqrt(n) ~ N(0,1)
mean of the sampling distribution ( x ) = 673
standard Deviation ( sd )= 32/ Sqrt ( 15 ) =8.2624
sample size (n) = 15

probability that their mean weight will be between 650 and 662 grams
To find P(a <= Z <=b) = F(b) - F(a)
P(X < 650) = (650-673)/32/ Sqrt ( 15 )
= -23/8.2624
= -2.7837
= P ( Z <-2.7837) From Standard Normal Table
= 0.0027
P(X < 662) = (662-673)/32/ Sqrt ( 15 )
= -11/8.2624 = -1.3313
= P ( Z <-1.3313) From Standard Normal Table
= 0.0915
P(650 < X < 662) = 0.0915-0.0027 = 0.0889