The overhead reach distances of adult females are normally distributed with a mean of 200 cm and a standard deviation of 7.8 cm.
a. Find the probability that an individual distance is greater than 209.30 cm.
b. Find the probability that the mean for 25 randomly selected distances is greater than 197.80 cm.
c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?
The overhead reach distances ( X ) of adult females are normally distributed
Mean = = 200 cm , standard deviation = = 7.8 cm
a )
We have to find P( x > 209.30 )
P( x > 209.30 ) = 1 - P( x <= 209.30 )
Using Excel function, =NORMDIST( x , mean , SD , 1 )
P( x <= 209.30 ) = NORMDIST( 209.30 , 200, 7.8 , 1 ) = 0.88343
So, P( x > 209.30 ) = 1 - 0.88343 = 0.11657
The probability that an individual distance is greater than 209.30 cm is 0.11657
b)
We have to find P( > 197.80 ) , sample size = n = 25
Mean of = 200
Standard deviation of = = = 1.56
P( > 197.80 ) = 1 - P( <= 197.80 )
Using Excel function, =NORMDIST( x , mean , SD , 1 )
P( <= 197.80 ) = NORMDIST(197.80 , 200 , 1.56 , 1 ) = 0.079232
So, P( > 197.80 ) = 1 - 0.079232 = 0.92077
The probability that the mean for 25 randomly selected distances is greater than 197.80 cm is 0.92077
c )
The normal distribution can be used in part (b) because the original population has a normal distribution.
The overhead reach distances of adult females are normally distributed with a mean of 200 cm...
The overhead reach distances of adult females are normally distributed with a mean of 195 cm and a standard deviation of 7.8 cm. a. Find the probability that an individual distance is greater than 204.30 cm. b. Find the probability that the mean for 15 randomly selected distances is greater than 193.50 cm. c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?
The overhead reach distances of adult females are normally distributed with a mean of 200 cm200 cm and a standard deviation of 7.8 cm7.8 cm. a. Find the probability that an individual distance is greater than 210.00210.00 cm.b. Find the probability that the mean for 2525 randomly selected distances is greater than 198.20 cm.198.20 cm. c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30? a. The probability is nothing.
The overhead reach distances of adult females are normally distributed with a mean of 205.5 cm and a standard deviation of 8.9 cm. a. Find the probability that an individual distance is greater than 215.50 cm. b. Find the probability that the mean for 15 randomly selected distances is greater than 204.00 cm. c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?
The overhead reach distances of adult females are normally distributed with a mean of 197.5 cm and a standard deviation of 8.3 cm. a. Find the probability that an individual distance is greater than 206.80 cm. b. Find the probability that the mean for 20 randomly selected distances is greater than 196.20 cm. c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?
The overhead reach distances of adult females are normally distributed with a mean of 205 cm and a standard deviation of 8.3 cm a. Find the probability that an individual distance is greater than 215.00 cm. b. Find the probability that the mean for 15 randomly selected distances is greater than 203.50 cm c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?
.4.6-T The overhead reach distances of adult females are normally distributed with a mean of 200 cm and a standard deviation of 8 cm a. Find the probability that an individual distance is greater than 212.50 cm. b. Find the probability that the mean for 25 randomly selected distances is greater than 198.70 cm c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30? a. The probability is Round to...
The overhead reach distances of adult females are normally distributed with a mean of 197.5 cm and a standard deviation of 8.3 cm. a. Find the probability that an individual distance is greater than 206.80 cm. b. Find the probability that the mean for 25 randomly selected distances is greater than 196.00 cm. c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30? a. The probability is (Round to four...
The overhead reach distances of adult females are normally distributed with a mean of 205 and a standard deviation of .7.8 a. Find the probability that an individual distance is greater than 215cm. b. Find the probability that the mean for 15 randomly selected distances is greater than 203.70 c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30? a. The probability is . 0999. (Round to four decimal places...
Question Help The overhead reach distances of adult females are normally distributed with a mean of 205.5 cm and standard deviation of 8.9 cm. a. Find the probability that an individual distance is greater than 218.00 cm. b. Find the probability that the mean for 15 randomly selected distances is greater than 203.70 cm. c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 3 a. The probability is .. (Round...
The overhead reach distances of adult females are normally distributed with a mean of 195 cm and a standard deviation of 7.8 cm a. Find the probability that an individual distance is greater than 204.30cm. b. Find the probability that the mean for 15 randomly selected distances is greater than 193.20 cm. c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30? a. The probability is (Round to four decimal...