Q1) Diameters of oranges in a certain orchard are normally distributed with mean of 4.85 inches and standard deviation of 0.40 inches.

a) What percentage of oranges in this orchard have diameters less than 4.3 inches?

b) What percentage of oranges in this orchard are larger than 4.75 inches?

c) Random sample of 100 oranges is gathered and mean diameter obtained was 4.75. If another sample of 100 is taken, determine s the probability that its sample mean will be greater than 4.75 inches?

d) Why is Z score utilized in answering (a), (b) and (c)?

e) Why is formulae for z used in (c) different from that used in (a) and (b)?

Q2) How does bell-shaped curve for sampling distribution of sample means for samples of size n =120 compare to bell-shaped curve for sampling distribution of sample means for samples of size n =95?

2) Consider binomial distribution with 14 identical trials, and probability of success of 0.4

i) Determine probability that x =3 using binomial tables.

ii) Utilize the normal approximation to determine the probability that x=3.