The phenotype of F1 progeny will be half wild type and half mutant . all the female rat will be wild type and all male rat in F1 will be mutant type.

The Phenotypes of F1 Progeny in a Cross between a Female Rat Homozygous for a Recessive X-Linked Mutation and a Male with Wild Type Phenotype

In order to understand the phenotypes of the F1 progeny resulting from the cross between a female rat homozygous for a recessive X-linked mutation and a male with a wild type phenotype, we need to consider the inheritance patterns of X-linked traits and the genotypes of the parents.

X-Linked Inheritance
X-linked inheritance refers to the transmission of genes located on the X chromosome. In mammals, including rats, females have two X chromosomes (XX) while males have one X and one Y chromosome (XY). Since males have only one copy of the X chromosome, any mutation present on this chromosome will be expressed phenotypically.

Female Rat Homozygous for a Recessive X-Linked Mutation
The female rat in this cross is homozygous for a recessive X-linked mutation. This means that both of her X chromosomes carry the mutant allele. As a result, she will express the mutant phenotype.

Male Rat with Wild Type Phenotype
The male rat in this cross has a wild type phenotype, indicating that he carries the normal allele for the gene in question on his X chromosome. Since males have only one copy of the X chromosome, they are hemizygous for X-linked genes.

F1 Progeny Phenotypes
The phenotypes of the F1 progeny can be determined by considering the genotypes of the parents and the inheritance pattern of X-linked traits.

- All of the female F1 progeny will inherit one X chromosome from the female parent, which carries the mutant allele, and one X chromosome from the male parent, which carries the normal allele. As a result, they will be heterozygous for the gene in question. These females will have a wild type phenotype because the presence of the normal allele masks the expression of the mutant allele.

- All of the male F1 progeny will inherit one X chromosome from the female parent, which carries the mutant allele, and one Y chromosome from the male parent, which does not carry the gene in question. Since males have only one copy of the X chromosome, they are unable to mask the expression of the mutant allele. As a result, the male F1 progeny will express the mutant phenotype.

In summary, the F1 progeny resulting from the cross between a female rat homozygous for a recessive X-linked mutation and a male with a wild type phenotype will consist of female rats with a wild type phenotype and male rats with a mutant phenotype.