In a Petri dish there are currently 1,235 bacteria. The growth rate of bacteria is 3.25% How many bacteria will be there in the
2 answers:
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Number of dimes collected is 339 and number of nickels collected is 113
<em><u>Solution:</u></em>
Given that There is a total of $39.55
There are 3 times as many dimes as nickels
To find: Number of dimes and nickels collected
Let "d" be the number of dimes collected
Let "n" be the number of nickels collected
We know that,
1 dime = $ 0.10
1 nickel = $ 0.05
From given information,
There are 3 times as many dimes as nickels
So, we get
Number of dimes = 3(number of nickels)
d = 3n
Given that there is total of $ 39.55
number of dimes collected x value of 1 dime + number of nickels collected x value of 1 nickel = $ 39.55
Substitute n = 113 in d = 3n
<em><u>Summarizing the results:</u></em>
number of dimes collected = 339
number of nickels collected = 113
Answer:
The answers to the questions are;
A) P(X) where x = 12 is equal to 3.55 ×10⁻²
B) P(x) using the normal distribution is given by the probability distribution function and is equal to 3.453 ×10⁻²
C) The calculated probabilities of P(x=12) using the binomial probability formula and the probability distribution function differ by 9.7×10⁻⁴
D) The normal distribution be used to approximate this probability because a. because np(1-p) %u2265 ⇒ np(1-p) ≥ 10
E) c. the value of fi represents the expected proportion of observation less than or equal to the ith data value.
Step-by-step explanation:
To solve the question, we note that
n = 58
p = 0.3
x = 12
Here we have n·p = 17.4 and n·q = 40.6 both ≥ 5 that is the normal distribution can be used to estimate the probability
A) We are to use the binomial probability formula to find P(X)
Where x = 12, we have P(12) = ₅₈C₁₂×0.3¹²×0.7⁴⁶
= 891794789340×0.000000531441×7.49×10⁻⁸ = 3.55 ×10⁻²
B) Using the standard distribution table we have
the z score for x = 12 given as = -1.55
From the normal distribution table, we have the probability that value is below 12 = .06057 while the normal probability distribution function which gives the probability of a number being 12 is given by
where:
σ = Standard deviation =
μ = Sample mean = n·p = 58×0.3 =17.4
Therefore the probability density function is
C) The probabilities differ by 3.55 ×10⁻² - 3.453 ×10⁻² = 9.7×10⁻⁴
D) The normal distribution be used to approximate this probability because n·p and n·p·(n-p) ≥ 5
E) f represents the area under the curve towards left of the ith data observed in a normally distributed population.
Therefore, the value of fi represents the expected proportion of observation less than or equal to the ith data value