Normal approximation to determine probability

Reference no: EM1313878

Q1) Diameters of oranges in the certain orchard are normally distributed with the mean of 7.3 inches and standard deviation of 0.80 inches. Illustrate all work.

(i) What percentage of oranges in this orchard have diameters less than 6.7 inches?

(ii) What percentage of oranges in this orchard are larger than 7.20 inches?

(iii) Random sample of 100 oranges is gathered and mean diameter got was 7.20. If another sample of 100 is taken, determine the probability that its sample mean will be greater than 7.10 inches?

(iv) Why is the z-score used in answering (A), (B), and (C)?

(v) Why is formula for z utilized in (C) different from that used in (A) and (B)?

Q2) Let a binomial distribution with 15 identical trials, and probability of success of 0.5

i) Determine probability that x = 2 using binomial tables

ii) Use normal approximation to determine probability that x = 2. Illustrate all work.

Reference no: EM1313878

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