Babies born at Memorial Southwest Hospital have weights that are normally distri

Question

Babies born at Memorial Southwest Hospital have weights that are normally distributed. The mean weight of the babies is 3200 grams with a standard deviation of 375 grams. a. What percent of babies weigh over 3600 grams? b. What percent of babies weigh less than 3450 grams? c. What percent of babies weigh between 2900 and 3300 grams? d. What is the weight of a baby that is at the 45 th percentile for weight? 2. The number of oranges that grow on an orange tree in Florida is normally distributed with a mean of 136 with a standard deviation of 21 oranges. a. What percent of the trees grow more than 140 oranges? b. What percent of trees grow between 90 and 110 oranges? c. What percent of trees grow less than 150 oranges? d. How many oranges does a tree grow if it is in the top 20% of orange producers?

Explanation / Answer

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1) Mean = 3200

s = 375

a) z = (3600 - 3200)/375 = 1.07

P = 14.23%

b) z = (3450 - 3200)/375 = 0.666

P = 74.54%

c) z1 = (2900 - 3200)/375 = - 0.8

z2 = (3300 - 3200)/375 = 0.27

P = 39.46%

d) z for 45th percentile = - 0.125

(x - 3200)/375 = - 0.125

x = 3153.13

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