Question

41. Find the area under the standard normal curve to the left of a, z= 1.18 b. z--1.85 c. 2-2.48 d. z-0.08 e, z=-1.25 g. z 0.05 h.-0.92 i. z- 0,00 j. z 3.24 4 Aert machn rodcas compoets havientinetes A of measuring samples of these components, it is found that the standard deviation is 0.2 centimeters. A test is carried out on a sample to check whether the data on the lengths of components is normally distributed and it found that this is so. a. the Determine the number of components likely to have a length of less than 14.95 cm in a of 10,000 components. b. Determine the number of components likely to be between 14.95 and 15.15 cm batch of 10,000 components. c. Determine the number of components likely to be larger than 15.43 em long in a batch of 10,000 components. Among a group of women aged 18-24 years, 808% are less than 61.2 inches tall, 90.13% are between 61.2 inches and 68.2 inches, and 1.79% are more than 68.2 inches tall. Assuming that the heights distribution can be adequately approximated by a normal curve, find the mean and the standard deviation of the heights. 43 44. The actual amount of coffee that a filling machine deposits into "6-ounce" jars varies from jar to jar, and may be looked upon as a random variable having a normal distribution with a standard deviation of 0.04 ounce. If only 2.5% of the jars are to contain less than 6 ounces of coffee, what must be the mean fill of these jars? If a set of grades on statistics quiz are approximately normally distributed with a mean of 74 and a standard deviation of 7.9, find: 45. a, the lowest passing grade if the lowest 10% of the students are given a failing grade of F's b, the highest B if the top 5% are given A's. 46. The cholesterol level X in healthy individuals is age- and sex-dependent. For males under age 21, the average reading of healthy individuals is 160 mg/dI with a standard deviation of 10 mg dl. For males 21-29 years old, the mean cholesterol level is 200 mg/dl with a standard deviation of 30 mg/dl, and for males 30 years or over, the mean cholesterol level reading is a standard deviation of 30 mg/dl. Assuming the cholesterol level follows a normal di find: a. the percentage of males under 21 years old whose cholesterol level is 170 mg/dl and above b. P195x224) among males whose ages are between 21 to 29 years old. 108 MATHEMATICS IN THE MODERN WORLD

Answer 1

41. answer

(a) z=1.18 = > 0.8810

B. z= -1.85 => 0.0322

c. z =-2.48 => 0.0066

d. z= 0.08 => 0.4681

e. z= -1.25 => 0.1056

f . .z= -0.24 => 0.4052

g. z=0.05 =>0.5199

h. z=0.92 =>0.8212

i z= 0.00 =>0.5000

j z= 3.24 =>0.9994

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