Question

**Report
results to 5 significant figures.**

**Show all
units of measurement as appropriate.**

3. What (**a,b**) are the two parameters of any
binomial distribution? Using these parameters, what
(**c, d**) are the expressions used for calculating
the mean and standard deviation of a binomial
distribution? In order to be able to approximate a
binomial distribution using a Normal distribution, (**e,
f**) what are the two criteria that must be
met? In one of Gregor Mendel’s genetics experiments, he
expected 75% of pea plants resulting from a particular cross to
bear green pods. (**g**) What was the
expected proportion of plants bearing green
pods? (**h**) What was the expected
proportion of plants bearing non-green pods? If he had a
total of 580 plants in this particular experiment,
(**i**) what number of plants would he have expected
to bear green pods? In fact, 428 plants bore green
pods. First, (**j, k**) check the validity
of using a Normal approximation to the binomial for the data from
this experiment. Then, assuming*p*= 0.75 and
using a Normal approximation to the binomial, (**l**)
calculate the probability of obtaining exactly 428 plants bearing
green pods. Since the result of 428 is fewer than 435,
(**m**) calculate the probability that, out of 580
plants, 428 or fewer would bear green pods, again assuming that
*p*= 0.75. (Observe the need to use the
continuity correction for parts (l) and
(m)). (**n**) Is the probability of
428 or fewer plants bearing green pods unusual, in a statistical
sense? (**o**) Which probability calculated
above is more useful in determining whether Mendel’s claimed
proportion of 75% is incorrect (state “l” or
“m”). **15**

Answer #1

* R-commands and
outputs*:

> 0.75*580

[1] 435

> p=0.75

> q=1-p

> n=580

> pbinom(428,n,p)

[1] 0.2649558

> O=428

> Z=(O-n*p)/sqrt(n*p*q)

> Z

[1] -0.6712486

> pnorm(Z)

[1] 0.2510311

### Rough

> pbinom(440,n,p)

[1] 0.6990141

> pbinom(441,n,p)

[1] 0.7318279

> pbinom(442,n,p)

[1] 0.7627857

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 9 minutes ago

asked 29 minutes ago

asked 36 minutes ago

asked 40 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago