Question

PART A: A particular fruit's weights are normally distributed, with a mean of 451 grams and a standard deviation of 29 grams. The heaviest 14% of fruits weigh more than how many grams? Give your answer to the nearest gram.

B) Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1.

If P(−b<z<b)=0.4434P(-b<z<b)=0.4434, find b.

C) A distribution of values is normal with a mean of 21.1 and a standard deviation of 88.3.

Find P₄₃, which is the score separating the bottom 43% from the top 57%.
P₄₃ =

Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answer 1

B) Here we need to find

So

Hence

Using z table we get such that

So

C) Here we need to find x such that

Using z table we get

So

Hence