The grades of STA220 are normally distributed with mean 70 and standard deviatio

Question

The grades of STA220 are normally distributed with mean 70 and standard deviation 10. a) What is the probability that a student can get more than 90. b) Find the 90th percentile [i e. find the grade such that 90% of grades fall below this grade and 10& fall above) A survey was conducted to measure the number of hours per week adults spend on home computers. In the survey, the number of hours were normally distributed, with mean of 7 hours and a standard deviation of 1 hour. Find the probability that the hours spent on the home computer by the participant are less than 4.5 hours per week. Suppose the scores x on a college entrance examination are normally distributed with a mean of 550 and a standard deviation of 100. A certain prestigious university will consider for admission only those applicants whose scores exceed the 90^th percentile of the distribution. Find the minimum score an applicant must achieve in order to receive consideration for admission to the university. If the data are normal A histogram or stem-and-leaf display will look like the normal curve The meant plusminus s, 2s and 3s will approximate the empirical rule percentages The ratio of the interquartile range to the standard deviation will be about 1.3 A normal probability a with the ranked data on one axis and the expected z - scores from a standard normal distribution on the other axis, will produce close to a straight line

Explanation / Answer

Answer:

Example 1

a).

z value for 90, z =(90-70)/10 =2

P( x >90)= P( z >2)

= 0.0228

b).

z value for 90th percentile =1.282

x = mean+z*sd = 70+1.282*10 = 82.82

Example 2

z value for 4.5, z =(4.5-7)/1 =-2.5

P( x <4.5)= P( z < -2.5)

=0.0062

Example 3

z value for 90th percentile =1.282

x = mean+z*sd = 550+1.282*100

= 678.2

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