Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 10.3 years, and standard deviation of 2.4 years.
If 21 items are picked at random, 5% of the time their mean life will be less than how many years?
Give your answer to one decimal place.

A particular fruit's weights are normally distributed, with a mean of 645 grams and a standard deviation of 18 grams.If you pick one fruit at random, what is the probability that it will weigh between 631 grams and 666 grams. (Give answer to 4 decimal places.)

About 9% of the population has a particular genetic mutation. 1000 people are randomly selected.
Find the mean for the number of people with the genetic mutation in such groups of 1000. (Remember that means should be rounded to one more decimal place than the raw data.)

If a seed is planted, it has a 60% chance of growing into a healthy plant.
If 9 seeds are planted, what is the probability that exactly 2 don't grow?
(Give your answer as a decimal rounded to 3 places.)

Answer 1

This is a normal distribution question with

Sample size (n) = 21
Since we know that

Given in the question
P(X < x) = 0.05
This implies that
P(Z < -1.6449) = 0.05
With the help of formula for z, we can say that

x = 9.4386

This is a normal distribution question with

P(631.0 < x < 666.0)=?

This implies that
P(631.0 < x < 666.0) = P(-0.7778 < z < 1.1667) = P(Z < 1.1667) - P(Z < -0.7778)
P(631.0 < x < 666.0) = 0.8783342285842126 - 0.21834346397637566


This is a binomial distribution question with
n = 1000
p = 0.09
q = 1 - p = 0.91
Since we know that


This is a binomial distribution question with
n = 9
p = 0.6
q = 1 - p = 0.4
where

Exactly 2 don't grow means exactly 7 grew

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