Mathematics, 20.07.2020 06:01 amykookie24

The overhead reach distances of adult females are normally distributed with a mean of 205 cm and a standard deviation of 7.8 cm. A. Find the probability that an individual distance is greater than 218.40 cm. B. Find the probability that the mean for 15 randomly selected distances is greater than 202.80 cm. C. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?

Answers: 1

Show answers

Answers

Answer from: xxaurorabluexx

Given the mean = 205 cm and standard deviation as 7.8cm

a. To calculate the probability that an individual distance is greater than 218.4 cm, we subtract the probability of the distance given (i.e 218.4 cm) from the mean (i.e 205 cm) divided by the standard deviation (i.e 7.8cm) from 1. Therefore, we have 1- P(Z $\leq 1.72$ ). Using the Z distribution table we have 1-0.9573. Therefore P(X >218.4)= 0.0427.

b. To calculate the probability that mean of 15 (i.e n=15) randomly selected distances is greater than 202.8, we subtract the probability of the distance given (i.e 202.8cm) from the mean (i.e 205 cm) divided by the standard deviation (i.e 7.8cm) divided by the square root of mean (i.e n= 15) from 1. Therefore, we have 1- P(Z $\leq -1.09$ ). Using the Z distribution table we have 1-0.1378. Therefore P(X >202.8)= 0.8622.

c. This will also apply to a normally distributed data even if it is not up to the sample size of 30 since the sample distribution is not a skewed one.

Step-by-step explanation:

Given the mean = 205 cm and standard deviation as 7.8cm

c. This will also apply to a normally distributed data even if it is not up to the sample size of 30 since the sample distribution is not a skewed one.

Answer from: Quest

your answer would be 12

Answer from: Quest

Ithink it is15not sure tho

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 18:30, maren17

Logan wants to know how many skateboards have defective parts. he inspects 20,000 skateboards and keeps track of the number of defects per board. use his probability distribution table to find the expected value for defects on a skateboard.

Answers: 3

continue

Mathematics, 21.06.2019 22:00, mileto1798

Write a description of each inequality. 1. -5a + 3 > 1 2. 27 - 2b < -6 (this < has a _ under it) 3. 1/2 (c + 1) > 5 (this > has a _ under it)

Answers: 3

continue

Mathematics, 21.06.2019 23:10, robert7248

Aline has a slope of . which ordered pairs could be points on a parallel line? check all that apply. (-8, 8) and (2, 2) (-5, -1) and (0, 2) (-3, 6) and (6, -9) (-2, 1) and (3,-2) (0, 2) and (5,5)

Answers: 3

continue

Mathematics, 22.06.2019 00:00, chitteshchandra56

This circle is centered at the origin, and the length of its radius is 6. what is the circle's equation? a. x^2+y^2=36 b x^2+y^2=6 c x+y=36 d x^6+y^6=1

Answers: 2

continue

You know the right answer?

The overhead reach distances of adult females are normally distributed with a mean of 205 cm and a s...