Question

A random sample of 1000 tulips from a large cultivated field yields 847 purple flowers and 153 pink flowers.

Answer 1

Answer:

The frequency of the purple and pink alleles in this field population are 84.7% and 15.3% respectively.

Step-by-step explanation:

According to the law of large numbers, in probability concept, as we increase the sample size (n), the sample statistic value approaches the value of the population parameter.

For example, as the sample size increases the sample mean ($\bar x$) approaches the true population mean (μ).

Similarly, as the sample size is increased the the population proportion can be estimated by the sample proportion.

In this case, a random sample of n = 1000 tulips are selected.

Of these 1000 tulips, the number of purple flowers was 847 and the number of pink flower was 153.

Compute the proportion of purple flower as follows:

$P(purple)=\frac{847}{1000}=0.847$

The frequency of purple flower is 0.847.

Since, the sample size is quite large, this proportion can be used to estimate the true proportion of purple alleles.

Compute the proportion of pink flower as follows:

$P(pink)=\frac{153}{1000}=0.153$

The frequency of pink flower is 0.153.

Again since, the sample size is quite large, this proportion can be used to estimate the true proportion of pink alleles.

Thus, the frequency of the purple and pink alleles in this field population are 84.7% and 15.3% respectively.